Calculus 1- Teach Yourself Differentiation

Master the power rule for differentiation: compute derivatives of a x^n as a n x^{n-1}, handle constants as zero, and apply the sum and difference rules to combine multiple terms.

Practice problems on the power rule reinforce exponent and radical rules, converting between exponents and radicals, and differentiating expressions like x^n with negative and fractional powers.

Differentiate expressions using the power rule, convert radicals to exponent form, and handle negative powers. Practice expanding sums and applying derivative rules to polynomials and fractions.

Learn the product rule for differentiating the product of two or more functions, using f g' + f' g, and extend the rule to three-function products.

Apply the quotient rule to differentiate fractions by using the derivative of the numerator and denominator, subtracting their products, over the square of the denominator.

Learn the chain rule by differentiating the outer function while keeping the inside function intact, then multiply by the inside derivative, with examples using powers and square roots.

Master differentiating all six basic trigonometric functions, applying derivatives of sine, cosine, tangent, cotangent, secant, and cosecant with respect to x, including constants outside the functions.

Explore product rule applications for two- and three-function products with trig functions, deriving expressions using sine, cosine, tangent, and secant derivatives, power rules, and identities like cosine 2x.

Learn to apply the quotient rule to derivatives of expressions with x and trig functions, derive the numerator and denominator, and simplify using sin^2 x + cos^2 x = 1.

Master the chain rule for differentiating composite trig functions by differentiating the outside function and multiplying by the inside derivative, with cot and cos examples.

Master the chain rule for trig functions by differentiating composite expressions like sine and cosine with square roots, using outer and inner function rules and the power rule.

Apply the quotient rule and product rule to differentiate trig expressions using the chain rule, with explicit steps and answers provided.

Learn to differentiate exponential functions, focusing on base e and general base a, using d/dx a^x = a^x ln a and applying product and quotient rules through examples.

Master the chain rule for exponential functions, differentiating expressions like e^{g(x)} and a^{f(x)} by multiplying the derivative of the outside function by the derivative of the inside.

Master derivatives of exponential functions with trig arguments by applying product and chain rules, including multiple-function and three-function product cases.

Master derivatives of logarithmic functions, including natural log and log base b, by applying the chain rule: d/dx log_b(u) = u'/(u ln b).

Discover derivatives of logarithmic functions, including log base seven and natural log, apply chain and product rules, and differentiate exponential functions with a composite inside.

Explore derivatives of logarithmic functions, including natural logs and base-three logs, using chain and power rules. Practice differentiating complex log expressions with 22 problems and solutions.

Explore the differentiation of logarithmic and trigonometric functions using the chain rule, deriving formulas for natural log, log base changes, sine, cosine, and tangent derivatives.

Differentiating products involving exponential, logarithmic, and trigonometric functions, this part 2 lecture applies the product rule and chain rule with trig identities to simplify results.

Explore differentiation of logarithmic and trigonometric functions, applying the derivative of natural log, power rules, and sine-cosine relationships through inside functions and denominators.

Revision of chain rule explains differentiating a composite function where y equals f(u(x)) by treating inner and outer functions, applying power rule, and computing dy/dx as dy/du times du/dx.

Apply the chain rule to differentiate composite functions by multiplying the derivative of the outer function by the inner function's derivative, with examples for trig, exponential, and logarithmic forms.

Master differentiation through practice problems applying power, product, quotient, and chain rules to differentiate composite functions, simplify results, and handle inside-function derivatives.

Practice differentiating using product and chain rules on composite inside/outside functions, with sine, cosine, cotangent, and e^(-x) cases. This set includes 25 problems with solutions for self-check.

Learn the derivatives of inverse trig functions and apply the chain rule to inner functions. Derive formulas for arcsin, arccos, arctan, and related functions with inner substitutions.

Explore derivatives of inverse trig functions, applying power, product, and inside-function rules to arcsin, arccos, and arctan, with step-by-step differentiation examples.

Explore derivatives of hyperbolic trig functions, highlighting how hyperbolic cosine and sine derivatives differ, and apply the chain rule to hyperbolic functions and their composites.

Explore derivatives of hyperbolic trig functions using chain, product, and quotient rules, deriving expressions for hyperbolic tangent, cotangent, secant, and related ratios.

Learn to differentiate inverse hyperbolic trig functions by applying the chain rule, product rule, and memorized formulas. Work through examples to solidify understanding.

Learn how to differentiate implicit functions by applying implicit differentiation: differentiate each term with respect to x, use product and chain rules, and solve for dy/dx.

Master implicit differentiation with exponential and logarithmic functions, using quotient, product, and chain rules to solve for y'. See examples with ln(xy) and e^(x−y) and practice problems with solutions.

Learn implicit differentiation of functions in x and y, applying chain rule, and product and quotient rules to find dy/dx in equations like x^2+y^2=2 and cases with trig functions.

Master differentiation of implicit relations involving trig functions by applying chain rule, quotient rule, and trig identities while differentiating with respect to y and solving for dy/dx.

Learn how to differentiate difficult power functions using logarithmic differentiation, including y = x^x and y = x^(−1/x), by taking logs, bringing down exponents, and applying derivatives.

Use logarithmic differentiation to compute derivatives of complex functions, taking logs on both sides, handling inner functions, and applying double logarithms when necessary, with practice problems.

Apply logarithmic differentiation to functions with variable base and exponent, using implicit differentiation, product and chain rules, to differentiate cases like x^y and y^x.

Learn to differentiate using logarithmic differentiation and implicit differentiation, apply derivatives of log x, and prove y' = y/x while solving problems with natural logs.

Apply logarithmic differentiation to complex functions with trigonometric components, using log both sides, differentiate log terms, and manage products and powers for accurate derivatives.

Master logarithmic differentiation to differentiate products of two or three functions, including cosine and sine, and decide when to use the quotient rule or logarithmic differentiation.

Learn to apply logarithmic differentiation to differentiate complex functions composed of products, quotients, and multiple parts, making difficult problems straightforward and faster.