# Differentiable functions.

• Nov 17th 2009, 02:19 PM
Rumor
Differentiable functions.
There's an annotation when it comes to differentiable functions that confuses me and I'm not sure what the difference is.

One is $\displaystyle f(x)={\sqrt(f(x)) }$ and the other is $\displaystyle f(x)=f{\sqrt(x) }$.

I know how to find the derivative of the first, but how is the second one different, and how do you find its derivative?
• Nov 17th 2009, 02:47 PM
Defunkt
Quote:

Originally Posted by Rumor
There's an annotation when it comes to differentiable functions that confuses me and I'm not sure what the difference is.

One is $\displaystyle f(x)={\sqrt(f(x)) }$ and the other is $\displaystyle f(x)=f{\sqrt(x) }$.

I know how to find the derivative of the first, but how is the second one different, and how do you find its derivative?

I assume for the second you mean $\displaystyle f(\sqrt{x})$.

If so, simply use the chain rule. Let $\displaystyle g(x) = \sqrt{x}, u(x) = f(g(x))$, then:

$\displaystyle u'(x) = f'(g(x))\cdot g'(x)$