3.5 Chain Rule

Try this: Find if , right? What about this: Isn’t this the same function as the previous slide, simply written differently? How do we get the same answer from this expression? By the power rule, it should like - where does the extra “4” come from?

The Chain Rule There are 2 versions: 1. This says: If you see a function within a function, take the derivative of the outside function times the derivative of the inside.

Example of V1 Find if Derivative of the inside – g’(x)

The Chain Rule The second version 2. This says: if y is a function of u, and u is a function of x, then the derivative of y in terms of x will be the derivative of y in terms of u times the derivative of u in terms of x. At the end, sub in the x expression in for u.

Example of V2 Find if and

Deriv of f(x) “outside” Example Find if and Method 1: Method 2: Deriv of f(x) “outside” Deriv of g(x) “inside”

Just follow the directions!!