Chain rule problem

**Kakariki** · February 21st 2010, 07:09 AM

Hey, I have a question that I do not know how to go about answering.

Question:
Let $y = g(h(x))$ where $h(x) = \frac{x^2}{x+2}$ . If $g'(9/5) = -2$ , find dy/dx when $x = 3$

Attempted answer:
Basically I have found the derivative of $h(x) = \frac{x^2}{x+2}$ . Which is $h'(x) = \frac {-x^2}{(x + 2)^2} + \frac {2x}{(x+2)}$

I do not know what I am supposed to do with $g'(9/5) = -2$ . How do I find what the function g(x) is from that?

Thanks!

**Ted** · February 21st 2010, 07:13 AM

Originally Posted by Kakariki

Hey, I have a question that I do not know how to go about answering.

Question:
Let $y = g(h(x))$ where $h(x) = \frac{x^2}{x+2}$ . If $g'(9/5) = -2$ , find dy/dx when $x = 3$

Attempted answer:
Basically I have found the derivative of $h(x) = \frac{x^2}{x+2}$ . Which is $h'(x) = \frac {-x^2}{(x + 2)^2} + \frac {2x}{(x+2)}$

I do not know what I am supposed to do with $g'(9/5) = -2$ . How do I find what the function g(x) is from that?

Thanks!

Start by this:
If $y=g\left(h(x)\right)$ then $y'=g'\left(h(x)\right) h'(x)$ .

**Kakariki** · February 21st 2010, 07:54 PM

Thanks, that's the chain rule. I have figured out that g'(9/5) basically is the same thing as $\frac {(3)^2}{(3) + 2)}$ (subbing 3 in for x). What does this tell me? I still do not understand how to find what g(x) is.

Basically asking for a more detailed explanation.

Thanks for the response though!

**HallsofIvy** · February 22nd 2010, 12:54 AM

Originally Posted by Kakariki

Thanks, that's the chain rule. I have figured out that g'(9/5) basically is the same thing as $\frac {(3)^2}{(3) + 2)}$ (subbing 3 in for x). What does this tell me? I still do not understand how to find what g(x) is.

It tells you the answer! The problem says NOTHING about finding g(x) and there is no reason to do that. f(3)= 9/5 so the derivative of g(f(x)), at x= 3 is g'(9/5)f'(3).

Basically asking for a more detailed explanation.

Thanks for the response though!

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