Since the Chain Rule is one of the most important derivative rules in all of calculus, it is important to have some practice using it in solving the derivative of various functions. In this video I combine the chain rule, product, and quotient rules to determine the derivatives of some very useful examples.

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Derivative Examples using the Chain Rule

Recap on the Chain Rule

All Examples

1. f(x) = sin⁡(cos⁡(tanx))
2. f(x) = e^sin⁡(3x)
3. f(x) = [(x-2)/(2x+1 )]⁹
4. f(x) = (2x+1)⁵(x³-x+1)⁴

Example 1

f(x)= sin⁡(cos⁡(tanx))

Solution:

Example 2

f(x) = e^sin⁡(3x)

Solution:

Example 3

Solution:

Example 4

f(x) = (2x+1)⁵(x³-x+1)⁴

Solution: