Question

CALCULUS HELP!!! PLEASE

Answer 1

Given f and g are differentiable function and
f(a)=-4, g(a)=c, g(c)=10, f(c)=15, f'(a)=8, g'(c)=5, f'(c)=6

If h(x)=f(g(x)), find h'(a)

Answer 2

Hey there :) Remember how to apply your chain rule?

Answer 3

yes

Answer 4

\[\Large\rm \frac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)\]This look familiar?
This is how we differentiate a composition.

Answer 5

Therefore if,\[\Large\rm h(x)=f(g(x))\]Then,\[\Large\rm h'(x)=f'(g(x))\cdot g'(x)\]

Answer 6

And we want to evaluate this function h at x=a.

Answer 7

\[\Large\rm h'(\color{orangered}{a})=f'(g(\color{orangered}{a}))\cdot g'(\color{orangered}{a})\]

Answer 8

Hmm let's start on the right side.
g'(a) = ?

Answer 9

Oh they didn't give us that :O Interestingggg

Answer 10

b

Answer 11

b? Ok I'll take your word for it :D
It's not listed above, but maybe you forgot to list some of them.

Answer 12

\[\Large\rm h'(\color{orangered}{a})=f'(g(\color{orangered}{a}))\cdot b\]

Answer 13

For a composition, work from the inside outward.\[\Large\rm h'(a)=f'(\color{royalblue}{g(a)})\cdot b\]How bout that g(a) part? Can we replace it with something?

Answer 14

c

Answer 15

\[\Large\rm h'(a)=f'(\color{royalblue}{c})\cdot b\]Good good good.

Answer 16

so it is 6b! :D

Answer 17

Yay team! \c:/
Good job!

Answer 18

thanks

Answer 19

no probsss