# Derivative of reciprocal functions

• Jun 4th 2008, 01:08 PM
SportfreundeKeaneKent
Derivative of reciprocal functions
Hi, I have a question asking: "f(x) is a differentiable function. Find the derivative of the recip. function g(x) = 1/f(x) at those points where f(x) does not = 0."

What exactly am I finding the derivative of here? g'(x) = -1/f(x)^2?
• Jun 4th 2008, 01:15 PM
Jhevon
Quote:

Originally Posted by SportfreundeKeaneKent
Hi, I have a question asking: "f(x) is a differentiable function. Find the derivative of the recip. function g(x) = 1/f(x) at those points where f(x) does not = 0."

What exactly am I finding the derivative of here? g'(x) = -1/f(x)^2?

use the chain rule: $\displaystyle g'(x) = - \frac {f'(x)}{[f(x)]^2}$ ...you'd get the same thing using the quotient rule
• Jun 4th 2008, 01:19 PM
Aryth
Due to the numerator being the derivative of f(x), f(x) must be differentiable, which is why it mentions it in the problem. It can throw some people off. But it's necessary information.
• Jun 4th 2008, 02:21 PM
Jhevon
Quote:

Originally Posted by Aryth
Due to the numerator being the derivative of f(x), f(x) must be differentiable, which is why it mentions it in the problem. It can throw some people off. But it's necessary information.

indeed. and of course g(x) is undefined if f(x) is 0, which is why we are also told this is not the case