Thread: Finding F'(a) and G'(a)

Suppose and
Also suppose

Find

and


To be honest I really don't have any idea what its asking or more of what its giving me and how to use it. Any help will be great thanks.

Hello, UMStudent!

This is an exercise in handling the Chain Rule.

Suppose: .F(x) = p(x^9) .and .G(x) = [p(x)]^9

Also suppose: .a^8 = 6, .p(a) = 2, .p'(a) = 13, .p'(a^9) - 15

Find: .(a) F'(a) .and .(b) G'(a)

(a) We are given: .F(x) .= .p(x^9)

Differentiate: .F'(x) .= .p'(x^9) · 9x^8

Then we have: .F(a) .= .p'(a^9) · 9a^8
. . . . . . . . . . . . . . . . . . . .↓ . . . . ↓
Substitute: . . . F(a) .= . . .15 · 9 · 6 . = . 810


(b) We are given: .G(x) .= .[p(x)]^9

Differentiate: .G'(x) .= .9[p(x)]^8 · p'(x)

Then we have: .G'(a) .= .9[p(a)]^8 · p'(a)
. . . . . . . . . . . . . . . . . . . . . ↓ . . . . ↓
Substitute: . . . G'(a) .= .9 · (2^8) · 13 . = . 29,952

great, thanks alot for all your help.