Use the table below to evaluate d/dx[f[g(2x)]] at x = 1

Question

brookemariexx · Answer

attachment

questionaskerduh1243 · Answer

20 is your answer

brookemariexx · Answer

How did you get this answer?

questionaskerduh1243 · Answer

one second

sunnnystrong · Answer

@brookemariexx ...
This is a composite function:

the derivative of f composed with g... evaluated @ x=1
$$\frac{ d }{ dx }f(g(2x))$$
$$\frac{ d }{ dx }f(g(2(1)))$$
Note that * g(2)=4...
So:
$$\frac{ d }{ dx }f(4)$$
Note that * f'(4)= 2

So.. it's 2.

sunnnystrong · Answer

At least im pretty sure.... @QuestionaskerDUH1243 how'd you get 20?

brookemariexx · Answer

thank you so much!
this was my answer: 
d/dx(2x)= 2
2*g'(2x)*f'(g(2x))
2*5*f'(4)
2*5*2=20
but not sure now?

questionaskerduh1243 · Answer

Well (2x)'=2 and the derivative of g is g' and derivative of f is f' so you have 2*g'(2x)*f'(g(2x)) Then input 1 for x

questionaskerduh1243 · Answer

Actually

questionaskerduh1243 · Answer

I was thinking that was right my bad i did my math wrong

questionaskerduh1243 · Answer

2 is correct

sunnnystrong · Answer

@brookemariexx 
this is a composite function. You don't really need to take the derivative of anything.. as you don't have a function only values to work with based on the table.

brookemariexx · Answer

Okay, thank you so much i understand now

questionaskerduh1243 · Answer

Yeah i wasnt thinking write i got up maybe 30 mins ago

questionaskerduh1243 · Answer

right*

sunnnystrong · Answer

NP :D Always happy to help out if I can!!