Posted by Lauren on Wednesday, April 1, 2009 at 6:40am.
I finished this problem but I wanted some feedback because I don't know if it's entirely correct.
Suppose that functions f and g and their derivatives with respect to x have the following values at x=2.
Find d/dx of f(g(x)) at x=2.
I know the chain rule is this:
f'(g(x)) * g'(x)
So you would write the derivative of the outer function, keeping the inner function (g(x)) as the 'x' value. But in this case, the derivative of the outer function is a number.... I wasn't sure how to approach this problem. How do I figure in the g(x)?
This is the answer (and work) that I got:
f'(g(x)) * g'(x)
1/3 * -3 = -1
Where 1/3 is f'(x) and -3 is g'(x). But I feel like this is incorrect, because I didn't input the value of g(x).
Does anyone know if what I did was right, or how to correct it if it was wrong? I wasn't given an equation for f(x) or g(x) so I assumed we were supposed to rely on the numbers given. Do I need to multiply f'(x) and g(x) to get 2/3?
- Calculus - Damon, Wednesday, April 1, 2009 at 9:00am
g(2) = 2
f'(2) = 1/3
f'(g(2)) = 2/3
g'(2) = -3
so I get
(2/3)(-3) = -2
- Calculus - Lauren, Wednesday, April 1, 2009 at 10:01am
Thank you! That makes more sense... because you would say f' of g of x.... so 1/3 of 2 = 2/3. That makes sense!
Answer this Question
More Related Questions
- Calculus Can you help - Suppose the functions f and g and their derivatives have...
- Math help/check - Suppose the functions f and g and their derivatives have the ...
- Calculus (Derivatives of Inverse Functions) - Suppose f(x) = sin(pi cos(x)). On ...
- Calculus - Hello, I really need help on these two homework problem. >< In ...
- Calculus: Derivatives - I'm having trouble understanding what derivatives in ...
- Math - suppose u and v are functions of x that are differentiable at x=2 and ...
- calculus-domain - Hello, I would greatly appreciate your input. I just need some...
- calculus - find the following derivatives: f(x) = (2x+5)/(x^2-3) f'(x)= (2)*(x^2...
- Calculus - Find the outside and inside functions of the following to find their ...
- calc - Find the derivatives of the following functions using the differentiation...