This week we reviewed on how to solve for the chain rule and when you have a chain rule, quotient rule, and product rule inside a chain rule or when you have a chain rule inside of a chain rule, quotient rule, or product rule. When you solve for the chain rule you use the formula d/dx f(g(x)) = f'(g(x)) X g'(x). in word form you take the derivative of the outside, then derivative of the outside then recopy the inside, multiply by derivative inside. Here’s an example of when you have to figure out what rule is first.

Example: d/dx -7/(2t-3)^2
1. Quotient Rule
2. Chain Rule

In this problem you would use the quotient formula first then take the chain rule and plug that in.
(2t-3)^2(0) - [(-7)(2(2t-3)^1(2)]/(2t-3)^4
28(2t-3)/(2t-3)^4
28/(2t-3)^3

Here’s an example of how you use the chain rule.

Example: d/dx (x^2 + 1)^3

3u^2 (2x)
3(x^2+1)(2x)
=6x(x^2+1)^2