Question

Use the given information to find f'(2). MEDAL WILL BE REWARDED!
g(2)=3 g'(2)=-2
h(2)=-1 h'(2)=4

f(x)=g(x)h(x)

Answer 1

@hartnn

Answer 2

use product rule

Answer 3

How do I incorporate these into this equation? Am I changing the equation first?

Answer 4

f'(x) = ... ?
then you just put x =2

Answer 5

okay so hold on give me one sec...

Answer 6

f(2)=3(2)-1(2)??

Answer 7

why 2 ?
\(\large f'= g'h +h'g \)
right ?

Answer 8

it was x so I thought I was subsitituing f(2)?

Answer 9

\(\large f'(x)= g'(x)h(x) +h'(x)g(x)\)
\(\large f'(2)= g'(2)h(2) +h'(2)g(2)\)
makes sense ?

Answer 10

oh okay, so I plug in h and g now?

Answer 11

yes, all values are given...

Answer 12

okay let me calculate

Answer 13

okay so before I go any further I have f'(2)=(-2)(2)(-1)(2)+(4)(2)(3)(2)

Answer 14

what ?
\(\large f'(2)= g'(2)h(2) +h'(2)g(2) \\ \large f'(2)=-2 (-1)+4(3)\)

Answer 15

oh okay....so my final answer would be f'(2)=2+12 so f'(2)=14?

Answer 16

yes.

Answer 17

Awesome! thank you, this one really was confusing!