# Homework Help: 2 Short questions

1. Oct 11, 2008

### DollarBill

1. The problem statement, all variables and given/known data
Let
g(5)=-3
g'(5)=6
h(5)=3
h'(5)=-2

Find f'(5) for f(x)=g(h(x))
Find f'(5) for [g(x)]3

3. The attempt at a solution
Find f'(5) for f(x)=g(h(x))
g'(h(x))*h'(x)
g'(3)*-2

But I don't know where to go from there because I'm not given g'(3).

Find f'(5) for [g(x)]3
I was thinking just to use the power rule, but it wasn't right
3g(x)2
3(-3)2

2. Oct 11, 2008

### Staff: Mentor

You had the right idea, but you lost you equation, and so lost your way.
2. Find f'(x). This should be an equation. f'(x) = ...
3. Evaluate f' at x = 5. f'(5) = ... To do this, you'll need the function values in your problem statement.
Mark

3. Oct 11, 2008

### SticksandStones

For the second one think of it like any ordinary chain rule problem. [g(x)]^3 = h(g(x)) where h(x) = x^3.

4. Oct 11, 2008

### DollarBill

I'm actually not quite sure what you mean...

2 Find f'(x): f'(x)=g'(h(x))*h'(x)
3.f'(5)=g'(h(5))*h'(5)
4.f'(5)=g'(3)*-2

And I'm pretty much where I was before...

5. Oct 11, 2008