Tuesday

March 31, 2015

March 31, 2015

Posted by **Lauren** on Wednesday, April 1, 2009 at 6:40am.

Suppose that functions f and g and their derivatives with respect to x have the following values at x=2.

f(x)=8

g(x)=2

f'(x)=1/3

g'(x)=-3

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?

Thank you

- Calculus -
**Damon**, Wednesday, April 1, 2009 at 9:00amf'(g(x))* g'(x)

g(2) = 2

f'(2) = 1/3

so

f'(g(2)) = 2/3

and

g'(2) = -3

so I get

(2/3)(-3) = -2

- Calculus -
**Lauren**, Wednesday, April 1, 2009 at 10:01amThank 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**

**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...