Question

f(2) = -8 , f'(2)=3 , g(2) = 17 and g'(2) = -4 what is the value of (f g)' (2)

Answer 1

\[f(g(2))\]

Answer 2

\[f'(g(2))\]
\[f(g'(2))\]

Answer 3

We can use the chain-rule to figure such out:
We know:
\[
(f(g(x)))'=f'(g(x))g'(x)
\]So, try that, see if helps

Answer 4

which one is it?

Answer 5

is that asking the derivative of the product of the two functions?

Answer 6

That's asking for composition, I think, since we have\[
(f\circ g)'(x)
\]

Answer 7

if it is the composition, then your stuck because the problem does not say anything about \(\large f'(17)= \) ?????

Answer 8

@LolWolf what would f'(17) be?

Answer 9

-204?

Answer 10

I think it's supposed to be a product? (f*g) ' ?

Answer 11

I did and thats what I got @Algebraic!

Answer 12

I think earlier replies were assuming it was a composition...

Answer 13

What is a composition ?

Answer 14

f( g(x) )

Answer 15

as opposed to f(x) * g(x)

Answer 16

answer is 83?

Answer 17

Can you show me how you got there?

Answer 18

product rule : (f*g) ' = f' *g + f* g'

Answer 19

=3*17 + (-8)*(-4)

Answer 20

And it is (fg)' (2) so 166?

Answer 21

83

Answer 22

But the question is Value of (fg)' (2) what do you do with the 2 then?

Answer 23

naw, that's the value of x at which they want you to evaluate the expression

Answer 24

ie at x=2 (f*g) ' = ...?

Answer 25

as far as I can tell from your problem statement...

Answer 26

Okay I see what you did there! Thanks

Answer 27

np:)