Calculus I (Differential Calculus)

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Videos on a first course in calculus (Differential Calculus).

638 students enrolled

What Will I Learn?

- Take the derivative of polynomial, rational, natural exponential, logarithmic, trigonometric, and inverse trigonometric functions.
- Understand how to use the product, quotient, and chain rule.

Requirements

- You should have taken Algebra I, Algebra II, Geometry and a Precalculus Course.

Description

Calculus I is designed primarily for those students planning to pursue programs in engineering, mathematics, computer science, and physical sciences. This course includes topics of differential and integral calculus of a single variable. This course contains a series of video tutorials that are broken up in various levels. Each video builds upon the previous one.

In this first course in Calculus (Differential Calculus) you will learn various differentiation rules that will allow you to find derivatives without the direct use of the limit definition. We will first learn how to find the derivative of polynomials and natural exponential functions.

Then we will shift gears and learn how to apply the product and quotient rule. We will then learn how to find the derivative of trigonometric functions. After that, we will learn how to use the chain rule to find the derivative of more complicated functions.

We will then learn how to differentiate via implicit differentiation. We will follow up with derivatives of inverse Trigonometric Functions and logarithmic functions. We will end the video series by learning how to differentiate via logarithmic differentiation.

After going over these videos you should be armed with the basic skills necessary to find the derivative of various functions.

Who is the target audience?

- College Students or high school students taking a first course in calculus.

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Curriculum For This Course

23 Lectures

03:08:49
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Introduction
1 Lecture
01:13

Preview
01:13

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Derivatives of Polynomials and Natural Exponential Functions
3 Lectures
25:15

This video introduces basic differentiation rules to find the derivative of polynomials and natural exponential functions. This video covers the derivative of a constant, the power rule, and the derivative of a natural exponential function.

Preview
10:04

This video will teach you the basics of calculating the derivative of simple polynomials and exponential functions using the constant multiple, sum and difference rule.

Derivatives of Polynomials and Natural Exponential Functions (Level 2)

07:30

This video will teach how to rewrite common functional expressions into a "derivative friendly" form. A good understanding of intermediate algebra is required to succeed in any calculus class.

Derivatives of Polynomials and Natural Exponential Functions (Level 3)

07:41

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The Product Rule
3 Lectures
27:46

This video will teach you how to find the derivative of functions formed by products of functions by using the product rule. An example involving the product of three functions is also illustrated.

The Product Rule (Level 1)

11:35

This video continues going over how to find the derivative of functions formed by products of functions by using the product rule. This videos goes over 5 examples illustrating how to find the derivative of functions by writing a general expression and using values that are provided to find the derivative at a given value of x.

The Product Rule (Level 2)

10:37

This video continues going over how to find the derivative of functions formed by products of functions by using the product rule. This videos goes over 2 examples illustrating how to find the derivative of functions by using the graphs of these functions.

The Product Rule (Level 3)

05:34

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The Quotient Rule
3 Lectures
28:55

This video will teach you how to find the derivative of functions formed by a quotient of functions by using the quotient rule and going over 3 examples.

The Quotient Rule (Level 1)

10:00

This video continuous going over more challenging example that require the use of the quotient. This video goes over 7 examples. 3 of these examples involves finding an expression for the derivative in terms of general functions.

The Quotient Rule (Level 2)

10:37

This is the third and final video on the quotient rule. This video goes over 4 examples illustrating how to find the derivative of a function by using a set of values and by using the graphs of functions.

The Quotient Rule (Level 3)

08:18

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Derivatives of Trigonometric Functions
1 Lecture
08:56

This video will teach you how to find the derivative of Trigonometric functions. In addition, this video will show you the graphical representation of the derivative in action!

Derivatives of Trigonometric Functions

08:56

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The Chain Rule
5 Lectures
37:28

This video will teach you the basics of the chain rule. It includes a small review of composition of functions and various examples demonstrating how to break apart a function into its composite functions.

The Chain Rule (Level 1)

06:27

This video will teach you how to find the derivative of simple composite functions by going over various examples using the chain rule in prime notation form and Leibniz form.

The Chain Rule (Level 2)

07:05

This video will teach you how to derive the derivative of exponential functions with base other than e. By using the chain rule you can derive the derivative of any exponential function. The video finishes of with 3 examples in the usage of the new derivative rule.

The Chain Rule (Level 3)

04:39

This video goes through various examples on derivatives that require the use of all the derivatives rules learned so far including the chain rule.

The Chain Rule (Level 4)

10:17

This video will teach you how to find the derivative of functions formed by a composition of 3 or more functions. This video is the last video in the chain rule series.

The Chain Rule (Level 5)

09:00

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Implicit Differentiation
2 Lectures
16:03

This video will teach you how to find the derivative of functions defined implicitly related by the dependent and independent variable.

Implicit Differentiation (Level 1)

06:20

This video will teach you how to find the derivative of functions defined implicitly. The video goes trough 6 different example of varying difficulty.

Implicit Differentiation (Level 2)

09:43

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Derivatives of Inverse Trigonometric Functions
2 Lectures
15:27

This video will teach you how to find the derivative of inverse trigonometric functions by implicit differentiation and algebraic manipulation.

Derivatives of Inverse Trigonometric Functions (Level 1)

08:50

This video will teach you how to find the derivatives of inverse trigonometric functions. The video goes trough 6 different example of varying difficulty.

Derivatives of Inverse Trigonometric Functions (Level 2)

06:37

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Derivatives of Logarithmic Functions
1 Lecture
10:27

This video will teach you how to find the derivatives of logarithmic functions. The video goes trough 7 different example of varying difficulty.

Derivatives of Logarithmic Functions

10:27

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Logarithmic Differentiation
2 Lectures
17:19

This video will teach you how to use logarithmic differentiation to find the derivative of complicated functions formed by products, quotients, and powers. The video goes trough 3 different examples.

Logarithmic Differentiation: Level 1

08:07

This video will teach you how to use logarithmic differentiation to find the derivative of functions where the base and exponent are them self's formed by functions. The video goes over various examples step by step.

Logarithmic Differentiation: Level 2

09:12

About the Instructor