The discussion revolves around finding the derivative f'(5) for two functions: f(x) = g(h(x)) and f(x) = [g(x)]^3, given specific values for g and h at x = 5.
Some participants have provided guidance on the differentiation process, while others express uncertainty about the next steps, particularly regarding the lack of information for g'(3). There is recognition of the need to evaluate expressions derived from the differentiation attempts.
Participants note the absence of a value for g'(3), which is critical for completing the derivative calculation for f'(5) in the context of the first function.
You had the right idea, but you lost you equation, and so lost your way.DollarBill said: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
I'm actually not quite sure what you mean...Mark44 said:You had the right idea, but you lost you equation, and so lost your way.
Mark
- Start with the equation for f(x). f(x) = ...
- Find f'(x). This should be an equation. f'(x) = ...
- Evaluate f' at x = 5. f'(5) = ... To do this, you'll need the function values in your problem statement.
Didn't see your reply before. Thanks, but I'm still not sure about the first one.SticksandStones said:For the second one think of it like any ordinary chain rule problem. [g(x)]^3 = h(g(x)) where h(x) = x^3.
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).DollarBill said: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...