Taylor Blog #5

This week we learned the chain rule and the general power rule
Im going to explain the Chain Rule,
The chain rule could loosely be defined as an order of operations that is used when solving composite functions.
A very important key concept to remember when using the chain rule is to work from the outside to the inside.
The “Formula” for the chain rule is
d/dx [fg(x)] = f ’(g(x)) (g’(x))
The most common procedure to using the chain rule is
• First, take the derivative of the outside
• Second, recopy just the inside
• Finally, multiply by the derivative of the inside
Example:
Square root of 3x^2-X+1
= (3x^2-X+1)^1/2
First, take the derivative of the outside:
½(________)^-1/2
Second, recopy just the inside
½(3x^2-X+1)^-1/2
Finally, multiply by the derivative of the inside
½(3x^2-X+1)^-1/2 (6x-1)
Simplify
6x-1/2(3x^2-x+1)^1/2


Another problem that may come up on the AP Exam that I feel I should include
The problems where we fill out the given chart for
Y= F(g(x))
U= g(x)
Y= f(u’)

Example:
Y= F(g(x)) U= g(x) Y= f(u’)
Y=(5x-8)^4 U=5x-8 y=u^4

I just thought I’d include this example because it helps you to understand the composition of an equation.