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

[DollarBill]

Homework Statement

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

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

 

[Mark44]

Homework Statement

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

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

You had the right idea, but you lost you equation, and so lost your way.

1. Start with the equation for f(x). f(x) = ...
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

 

[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.

 

[DollarBill]

You had the right idea, but you lost you equation, and so lost your way.

1. Start with the equation for f(x). f(x) = ...
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

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

1. Start with equation: f(x)=(g(h(x))
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...

 

[DollarBill]

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

Didn't see your reply before. Thanks, but I'm still not sure about the first one.

I'm always wary of going with a "None of the above" type answer.

 

[Mark44]

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

1. Start with equation: f(x)=(g(h(x))
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...

Not really. You have an expression for f'(5). Take another look at the information that was given in the problem to make sure you have all of the given information and that you have included it in this thread. If so, and the problem didn't give you a value for g'(3), then you have done everything that you can and -2*g'(3) is the value for f'(5).
Mark