U3: Differentiation: Composite, Implicit, and Integral Functions

The Chain Rule

The chain rule helps us find the derivative of a composite function. For the formula, g’(x) would be the chain.

Example:

General Rule Power

We use the general rule power when finding the derivative of a function that is raised to the nth power. In the formula given, f’(x) is the chain.

Implicit Differentiation

Inverse Trig Functions: Differentiation

Example:

Derivatives of Inverse Functions

Find:

(a) The derivative of the inverse function at x=a

(b) The equation of the tangent line to the inverse function at the point x=a

Using the function f(x)=5-2x3 , a=7

Higher-Order Derivatives