Question

if f(x)= h(x)g(x), where g(0)=2, g'(0)=5, h(0)=3, and h'(0)=-9, find f'(0)
(step by step)

Answer 1

Use the product rule since you have a product.
(uv)'=uv'+vu'

Answer 2

After you have applied product rule you can then replace all the x's with 0
and use the values given to you to find f'(0)

Answer 3

am i supposed to do this........h(x)g(x)'+g(x)h(x)' @freckles

Answer 4

\[f'(x)=g'(x)h(x)+g(x)h'(x)\]

Answer 5

Usually people put the derivative sign thing directly behind the function name

Answer 6

do i plug in the zero's or the values into this function? @freckles

Answer 7

You want to find f'(0)
and f'(x)=g'(x)h(x)+g(x)h'(x)
so what do you think we need to replace x with?

Answer 8

zero

Answer 9

yes so do so

Answer 10

what takes place of the letters? @freckles

Answer 11

you mean what is g(0) and g'(0) and h(0) and h'(0)?

Answer 12

These values are all given to you in your question.

Answer 13

yes

Answer 14

am i supposed to do this...... f(o)=5(0)93(0))+2(0)(-9(0)) @freckles

Answer 15

woah..
wait...did you replace all the x's with 0's in the equation:
f'(x)=g'(x)h(x)+g(x)h'(x)

Answer 16

f'(0)=g'(0)h(0)+g(0)h'(0)

Answer 17

look at your question and look what is given to you

Answer 18

you are given g'(0) is 5 so replace g'(0) with 5
you are given h(0) is 3 so replace h(0) with 3
you are given g(0) is 2 so replace g(0) with 2
you are given h'(0) is -9 so replace h'(0) with -9

Answer 19

f'(0)=5(3)+2(-9)
f'(0)= -3
@freckles

Answer 20

exactly

Answer 21

thank you! @freckles