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Learn MoreCalculus 1-Learn complete concepts of Differential calculus
Rating: 4.6 out of 54.6(40 ratings)
546 students
Calculus 1-Learn complete concepts of Differential calculus
A course on Differential calculus that boosts your confidence and helps you solving problems of calculus with an ease.
Created bySandeep Kumar Mathur
Last updated 5/2026
English
English [Auto],
What you'll learn
- Students will learn basic concepts, Formulae, Important results and tips and tricks of Differentiation from basics to advance
- You will understand solution of selected and excellent questions step by step on each topic of Differential calculus
Explore related topics
Course content
21 sections • 191 lectures • 13h 54m total length
- Basic Concepts of Functions23:37
Explore fundamental concepts of functions, including domain, range, independent and dependent variables, and how unique associations define a function, with even, odd, and not-a-function examples.
- Graphs of real valued Functions12:27
Explore graphs of real-valued functions, including the identity and modulus (absolute value) functions, defined piecewise and shown with open and closed points, illustrating domain and range.
- Graphs of Exponential and Logarithmic Functions5:47
Explore the graphs of exponential and logarithmic functions, showing how bases a>0, a≠1 shape growth and decay, with y=a^0=1 and log_a(1)=0.
- Q.no. 14:49
Evaluate f(3) and f(4) for f(x) = sqrt(25 - x^2) and determine the domain, which is [-5, 5], since the radicand must be nonnegative.
- Q.no. 22:48
Identify and compute explicit values by simplifying algebraic expressions in x, including forms like 2x+5 and -2x-5, to reinforce basic manipulation in calculus foundations.
- Q.no. 31:28
Explore q.no. 3 in calculus 1, focusing on the caption’s discussion of expressway and powers, illustrating equal relationships in differential calculus.
- Q.no. 45:12
Apply properties of logarithms to transform and simplify a log expression, replacing variables, factoring, and comparing numerator and denominator to reveal a simpler value.
- Q.no. 52:05
Discusses problem five with symbolic references like B plus one and E plus one, illustrating a simple explanation and notes a plan B amid a political divide.
- Q.no. 62:58
Apply algebraic substitution and fundamental identities in a differential calculus question, using 1 minus x and x squared terms, with reminders to recall the key formula and review related material.
- Q.no. 76:02
Analyze how to apply logarithm properties to simplify and combine logarithmic terms, derive a solution form with constants, and check consistency with the given expression.
- Q.no. 81:59
Apply logarithm laws to simplify expressions involving x+1, x, and x−1. Conclude that the combined form equals log((x+1)/(x−1)).
- Q.no. 97:13
This lecture shows how to determine if a function is even, odd, or neither by testing f(-x) against f(x) and -f(x), with examples.
- Q.no. 104:02
analyze f(-x) using log and square root properties to test parity, and conclude the function is odd.
- Q.no. 111:37
This lecture analyzes a function by evaluating f(-x) and showing f(-x) = -f(x), concluding the function is odd and highlighting function transformations in differential calculus.
- Q.no.126:22
Explore how to determine the domain of a function by solving inequalities for x, showing that the valid values lie between 1 and 4 inclusive.
- Q.no.134:08
Determine the domain by excluding x-values that make the denominator zero. Then, identify the range by evaluating the function's outputs.
- Composite Functions11:52
Explore composite functions, defined as g∘f from A to C, with domain and range considerations; examine properties, examples showing when g∘f equals or differs from f∘g, and conditions for bijectivity.
- Q.no.12:08
Explore the composition of functions with f(x)=x^3 and g(x)=3x-1. Show that g∘f(x)=3x^3-1 and f∘g(x)=(3x-1)^3, and conclude that g∘f ≠ f∘g.
- Q.no.23:13
Demonstrate that f(f(x)) equals minus one over x for all x not equal to 0 or minus one by substituting f(x) into f and simplifying the resulting rational expression.
- Q.no.33:47
for f(x) = (3x-2)/(2x-3), prove that f(f(x)) equals x for all real x except 3/2. compose and simplify to reveal the identity.
- Quiz
- Basic Concepts of Limits and Formulae20:29
Explore limits, including left and right limits and neighborhood approaches, and apply limit laws to evaluate indeterminate forms using cancellation and standard formulas.
- Q.no. 14:43
Analyze the limit of |x-4|/(x-4) as x approaches 4 from both sides, revealing left-hand and right-hand limits and the overall limit behavior.
- Q.no. 23:34
Explore left- and right-hand limits at x=1 for a piecewise function, showing how the one-sided limits may differ and cause the overall limit to not exist.
- Q.no. 34:15
Explore the concept of limits in calculus, focusing on left-hand and right-hand limits as x approaches zero, and show how the two-sided limit may not exist.
- Q.no. 42:49
The lecture demonstrates finding the left and right limits at x = 1, showing both sides approach 1, so the limit exists and equals 1.
- Q.no. 52:01
Explore limit concepts in differential calculus, focusing on left and right limits, including zero minus and zero plus, and how these limits define function behavior.
- Q.no. 63:56
Analyze a piecewise function defined by 4x−5 on the left and x−λ on the right, determine left and right limits, and find λ for which the limit exists.
- Q.no. 74:21
Identify the odd function property f(x) = -f(-x) and its equivalent f(-x) = -f(x). Show that the limit of f(x) as x approaches zero from both sides is zero.
- Q.no. 82:23
Explore limits in differential calculus, focusing on even functions and evaluating left and right limits as x approaches zero. Understand when these limits coincide and relate to f(0).
- Methods of finding out Algebraic Limits : Direct Substitution2:21
Learn the direct substitution method to evaluate algebraic limits and determine the limit value by substituting x into the function, a core concept in differential calculus.
- Q.no. 12:23
Explore limits in differential calculus by evaluating polynomial expressions and substituting values, such as x=1 in 3x^2+4x+5, to determine limit values.
- Method of Factorisation1:37
Learn how to evaluate limits using the method of factorisation, identify common factors, and apply substitution to simplify expressions and solve calculus problems.
- Q.no. 13:38
Learn to factor quadratics using the splitting the middle term method, showing x^2 -5x +6 = (x-2)(x-3) and applying similar factoring to a limit involving x^2 -1.
- Q.no.28:07
Factor polynomials in the numerator and denominator, cancel common factors, and simplify a rational expression to evaluate a limit. Identify the limit value 3/16 from the final simplification.
- Q.no.35:40
Evaluate the limit as x approaches 2 by factoring the numerator and denominator, canceling the common x minus 2 term, and simplifying to obtain the limit equals 1.
- Q.no.44:41
This lecture demonstrates evaluating a rational limit by factoring numerator and denominator, canceling common factors such as x−1 and 2x−1 using difference-of-squares identities, then substituting to obtain a finite value.
- Q.no.51:46
Use first principles to evaluate a limit by factoring 1 minus x squared as (1+x)(1−x), applying a common denominator, canceling (1−x), and substituting x = 1 to obtain 1/2.
- Q.no.64:03
Evaluate the limit as x approaches 1 of a rational expression by factoring the denominator and canceling x-1, yielding the value -1.9.
- Q.no.73:42
The lecture shows how to evaluate the limit as x approaches 2 for (x^4 - 4)/(x^2 + 3x - 8) by factoring and canceling (x-2), then substituting x=2.
- Method of Expansion6:12
Explore the expansion method to evaluate limits by expanding e^x, e^{-x}, log(1+x), log(1-x), and binomial forms, and learn how these series reveal limit values.
- Q.no.12:07
Apply the expansion of log(1+x) base e to evaluate the limit as x tends to zero of log(1+x)/x, showing the limit equals 1.
- Q.no.21:38
Apply the sine series expansion to evaluate the limit as x tends to zero of sin x over x, showing higher-order terms vanish and the limit equals one.
- Quiz
- Continuity of Functions8:15
Explore continuity of functions by checking the definition at a and equal left and right limits, with polynomial function, exponential function, and absolute value function as examples.
- Q.no.12:43
Examine the limits of a function for specific x values, including x equals zero, x minus one, and two x plus one, within a differential calculus framework.
- Q.no.23:24
Examine left and right limits as x approaches zero, show they equal the function value, and conclude the function is continuous on the interval between minus one and one.
- Q.no.33:42
Promote understanding of limits and continuity in differential calculus by showing how the limit as x approaches zero fixes C with f(0)=1, yielding C^2=1 and C=±1.
- Quiz
- Differential coefficient of x^n by first principle9:01
Learn to find the differential coefficient of x^n using the first principle, derive the nx^{n-1} rule via binomial expansion, and apply the limit concept to differentiation.
- Differential coefficient of e^x by first principle4:47
Derive the differential coefficient of e^x from first principle, using the limit and exponential series 1 + x + x^2/2! + x^3/3! + ..., to show the derivative equals e^x.
- Differential coefficient of a^x by first principle4:47
Explore differentiating a^x using first principle, employing the exponential expansion and a zero-limit to derive the derivative. Conclude with d/dx a^x = a^x ln a.
- Differential coefficient of log x by first principle5:59
The lecture uses first principles and the expansion of log(1+x) to derive the differential coefficient of ln x as 1/x.
- Differential coefficient of sin x by first principle5:32
We derive the differential coefficient of sin x by first principles, using the limit of sin x over x to establish the derivative.
- Differential coefficient of cos x by first principle5:20
Derive the differential coefficient of cos x using first principles, applying the limit approach to establish the rate of change of cos x.
- Differential coefficient of tan x by first principle6:01
Derive the differential coefficient of tan x from first principles, using limits and sine and cosine concepts to explain its derivative.
- Other formulae1:11
Explore other formulae in differential calculus and apply them to practice problems, with guidance and support for solving your assignments.
- Differential coefficient of sin inverse x by first principle and other formulae7:51
Learn to compute the derivative of arcsin x from first principles and using core formulas, guided by the inverse-function concept. Apply inverse-trigonometric differentiation rules and related identities.
- Formulae and Rules of Differentiation7:04
Learn the differentiation formulae derived from first principles and master the rules of differentiation, including the power rule and derivatives of log and exponential functions.
- Chain Rule3:09
Master the chain rule and differentiation of functions of functions with examples and explanations to build confidence in differential calculus.
- Q.no. 13:44
Apply the chain rule to differentiate composite functions such as sin(x^2+5) with respect to x, and recognize functions of a function in differential calculus.
- Q.no. 20:59
Explore differential calculus concepts by differentiating between different methods, using numeric examples like minus four and plus eight to illustrate reasoning and problem-solving in calculus.
- Q.no. 32:53
Develop a habit of solving differentiation questions directly, reinforcing understanding of explicit methods. Differentiate the function y = sin x with respect to x, highlighting core differential calculus ideas.
- Q.no. 44:13
Master the power rule in differential calculus by differentiating x^n and applying the formula d/dx x^n = n x^{n-1}, with practice on basic differentiation.
- Q.no. 52:07
The lecture demonstrates solving a calculus problem using a formula to solve for x, and applies crosschecks to verify the solution.
- Q.no. 63:02
Apply differentiation rules to sine and exponential functions, work with power expressions like x squared, and verify derivative results to solidify concepts in differential calculus.
- Q.no. 73:04
This lecture analyzes the differentiation of the base function x^2 + x + 1 and its power forms, applying power rules to find derivatives.
- Q.no. 83:38
the lecture demonstrates differentiating different types of functions using derivative rules, including powers and negative exponents, and applying these rules to find derivatives.
- Q.no. 94:24
master differentiation with respect to x by applying the standard derivative formula and practice simplifying results such as 3x^2.
- Q.no. 1010:25
Differentiate a function with respect to x, analyze the inverse relationship for a one-to-one function, and apply derivative rules to expressions with squares, plus and minus terms, and simplification.
- Quiz
- Basic Concepts8:13
Learn basic differentiation concepts by applying standard substitutions to simplify expressions, including exponential substitutions x = e and various square forms, and study inverse relationships in the process.
- Q.no.13:12
Differentiate 1 minus x squared with respect to x, applying substitution and inverse relationships to simplify and obtain the derivative.
- Q.no.24:24
Master simplifying expressions and applying inverse operations in calculus, using trig identities like sine squared and cosine squared to solve and verify equations.
- Q.no.33:54
Learn differentiation techniques in calculus, including substitution and simplifying expressions with respect to x, and identify when derivatives equal zero.
- Q.no.41:52
Explore substitution techniques and inverse functions to transform and analyze functions involving x and y, including x^2 - 1 and x^2 - 4, in differential calculus.
- Q.no.53:07
Explore the basics of differential calculus using functions of x, including x squared, and derive formulas involving expressions like 1 minus x squared and square root denominators.
- Q.no.62:33
Explore how dividing the numerator and denominator reveals an inverse relationship in expressions. Connect these ideas to foundational concepts in differential calculus.
- Q.no.73:12
Explore a calculus problem (q.no.7) using a one minus a squared term formula, and learn how minus and plus components simplify expressions and guide sign analysis.
- Q.no.81:59
Analyze algebraic expressions involving one plus a square, signs, and equal terms to understand how values are computed in differential calculus.
- Q.no.93:04
Convert complex algebraic expressions into a universal form, analyzing expressions like one plus x and one minus x squared, and explore the related calculus notation and symbols.
- Q.no.103:00
Explore differential calculus concepts by differentiating functions such as 1−x and 1−x^2, applying derivative rules.
- Quiz
- Derivatives of Implicit Functions10:04
Learn to find the derivative of implicit functions using implicit differentiation when y cannot be isolated from x, and examine the relation between dy/dx and dx/dy.
- Q.no. 11:05
Learn differential calculus concepts with respect to x, including expressions in a standard formula and how they appear in the denominator.
- Q.no. 22:06
Explore basic differential calculus by differentiating with respect to x and expressing derivatives in alternate forms, including signs and fractional representations.
- Q.no. 32:02
Learn to differentiate Y with respect to X, analyze Y as a function of X, and handle cases with minus signs and division by X to compute the derivative.
- Q.no. 42:54
Learn to differentiate with respect to x, apply the standard derivative formulas, and work with functions where x and y relate through derivatives.
- Q.no.51:41
Explore differential calculus basics by differentiating both sides and applying the product rule with respect to x. Learn implicit differentiation and derivative rules to find d/dx for common functions.
- Q.no.62:50
Analyze question six in this differential calculus lecture, exploring how functions relate to x, how expressions use denominators, and how precision and equality are discussed.
- Q.no.74:23
Explore differentiation of the expression x^2 + y^2 using standard calculus rules. Apply differentiation with respect to the variables and discuss basic outcomes.
- Q.no.82:09
Practice implicit differentiation by differentiating both sides with respect to x and solving for the derivative from the implicit equation, aligning with question number nine.
- Q.no.92:22
Master differentiation with respect to x by examining x squared and related square terms, as part of learning complete differential calculus concepts.
- Q.no.104:59
Explore differentiation of expressions by treating them as explicit first and second functions, and apply explicit and implicit methods to logarithmic and exponential components.
- Q.no.115:20
From the equation sqrt(1+y) + sqrt(1+x) = 0 with x ≠ y, we derive y = -x/(x+1) and obtain dy/dx = -1/(x+1)^2.
- Q.no.124:10
Differentiate e^x + e^y = e^{x+y} using the chain rule, then use e^{x+y} = e^x e^y and algebraic rearrangement to solve for dy/dx.
- Quiz
- Q.no. 12:39
The lecture clarifies the differentiation formula for functions, detailing the roles of numerator and denominator, and notes domain restrictions where the denominator cannot be zero.
- Q.no. 21:44
Differentiate with respect to x for exponential functions like e^x, explore inverse functions, and apply standard differentiation formulas.
- Q.no. 31:23
Examine how x and y relate as a function, including squares and equalities, in the lecture caption. Apply differential calculus concepts to interpret these relationships.
- Q.no.43:16
Learn to perform implicit differentiation for functions expressed implicitly by differentiating with respect to x when the relation cannot be written explicitly.
- Quiz
- Basic Concepts of Logarithmic Differentiation5:34
Master the basics of logarithmic differentiation in calculus by applying the log-differentiation method to products, quotients, and composite functions for efficient derivative computation.
- Q.no. 16:27
Apply logarithm properties to simplify and differentiate functions with respect to x, using log rules to handle composite expressions in differential calculus.
- Q.no. 26:07
Learn to differentiate logarithmic expressions by applying log rules—log products, quotients, and powers—and differentiate the resulting single expression with respect to x.
- Q.no. 34:27
Learn how to differentiate the power function x^x by rewriting as e^{x ln x} and applying derivative rules to obtain d/dx x^x = x^x(ln x + 1) using natural logarithms.
- Q.no. 43:19
Differentiating with respect to x for a function of the form x to the power x is explained using logarithmic differentiation and converting to a logarithmic form.
- Q.no. 54:04
Explore how to differentiate the equation x^y = y^x by applying logarithms and implicit differentiation to obtain the derivative dy/dx.
- Q.no. 62:05
The lecture analyzes the infinite sum x + x + x + ... and why it equals one under certain conditions, then differentiates both sides with respect to x.
- Q.no. 75:19
Differentiate a composite function by differentiating the first function and then the second with respect to x, and incorporate logarithmic terms like log x.
- Q.no. 84:07
This lecture explores differentiation of functions, including derivatives of expressions like log x. It applies differentiation principles to combinations of x and y.
- Q.no. 94:35
Explore a differential calculus problem (question nine), highlighting differentiation with respect to x and using the logarithmic method to solve conditions.
- Q.no. 104:14
Explore algebraic manipulation of expressions involving minus and plus terms and division within differential calculus concepts.
- Q.no. 113:38
Explore the properties of the logarithmic function y = log x, focusing on base, positivity, and algebraic manipulation of log expressions. Apply these ideas to practice problems in differential calculus.
- Q.no.122:02
Explore differential calculus by differentiating functions with respect to a variable, including power and logarithmic forms, and applying differentiation rules to complex expressions.
- Q.no.132:42
Explore differentiation in calculus by differentiating logarithmic and composite functions. Practice differentiating log x and expressions involving 1 minus x with intuition and rigor.
- Q.no.143:48
Explore differential calculus concepts in question 14, focusing on differentiating logarithmic expressions such as log x and applying these ideas to calculus problems.
- Q.no.156:02
apply a simple method using logarithmic differentiation to a calculus problem, compare with standard differentiation, and derive a radius-related result from expressions like log(x+1).
- Q.no.1610:32
Explore differentiating a rational function by taking logs and differentiating: rewrite y as x^3/[(x−a)(x−b)(x−c)], and obtain dy/dx = (y/x)[a/(a−x) + b/(b−x) + c/(c−x)].
- Q.no.173:17
Apply logarithmic differentiation to y = 5^x / x^5 and obtain dy/dx = (5^x / x^5)(log 5 - 5/x).
- Q.no.184:12
Differentiate the product (x+1)^2 (x+2)^3 (x+3)^4 using logarithmic differentiation; take logs, differentiate, and obtain dy/dx = (x+1)^2 (x+2)^3 (x+3)^4 [2/(x+1) + 3/(x+2) + 4/(x+3)].
- Q.no.193:54
Uses logarithmic differentiation to differentiate y = e^x cos^3 x sin^2 x, obtaining dy/dx = e^x cos^3 x sin^2 x [1 - 3 tan x + 2 cot x].
- Quiz
- Basic Concepts5:28
Explore basic concepts of differential calculus, focusing on limits and the relationship between X and Y, and apply a simple formula with example problems to solve.
- Q.no. 11:40
Learn how to differentiate using the power rule and derivative formulas, applying them to power functions and recognizing x squared.
- Q.no. 21:13
Practice differentiation techniques in differential calculus using a formula involving x and y, as shown in the previous question. This lecture applies the division-based formula to solve for variables.
- Q.no.31:42
investigate differential calculus concepts through a discussion of parameters, formulas, and minus-sign transitions, highlighting how sign changes influence the presented mathematical relationships.
- Q.no.41:13
Explore differential calculus by understanding how to compute changes with respect to a variable, applying formulas to expressions involving x, constants, and squared terms.
- Q.no.52:33
Explore differentiation in calculus 1, with a focus on differentiating with respect to a variable and understanding derivatives and power terms.
- Q.no.63:45
Solve a radius x problem by applying a logarithmic formula and previously used methods to determine B and X.
- Q.no.71:28
Solve for x, y, and z using subtraction and equalities, and interpret the resulting relationships within a differential calculus context.
- Q.no.83:28
this lecture explores a differential calculus exercise with x squared and b squared, deriving x in terms of b and differentiating with respect to x to reinforce concepts.
- Q.no.93:08
Use chain rule: dy/dt = (dy/dx)(dx/dt). With y = x^3 - 8x + 7, dy/dx = 3x^2 - 8; at x = 3 and dx/dt = 2, dy/dt = 38.
- Quiz
Requirements
- You should have a decent foundation in Algebra.
- Some knowledge of Precalculus and Trigonometry will be helpful
Description
If you find it difficult to remember various formulas of Differential Calculus ? If you have a feeling of not being confident in Differentiation ? If you facing difficulty in solving calculus questions and feel that you need to strengthen your basics? Then you have come to the right place.
Calculus is an important branch of Mathematics. It helps in solving many problems arise in practical situations. Generally many questions do come from this topic in competition exams. The course is useful for both beginners as well as for advanced level. Here, this course covers the following areas in details:
Differentiation chain Rule
Derivatives of Implicit Functions
Derivatives of Exponential Functions
Logarithmic Functions
Derivatives of Functions in Parametric Forms
Second Order Derivatives
Each of the topic has a great explanation of concepts and excellent and selected examples.
I am sure that this course will be create a strong platform for students and those who are planning for appearing in competitive tests and studying higher Mathematics.
You will also get a good support in Q&A section . It is also planned that based on your feed back, new material like Limit and continuity, Application of derivatives etc. will be added to the course. Hope the course will develop better understanding and boost the self confidence of the students.
Waiting for you inside the course!
Who this course is for:
- Students who are studying Integral Calculus in their academic syllabus and wishes to learn it
- Students preparing for IIT JEE,NDA,MCA entrance exams.