1. ## 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 $f(x)={\sqrt(f(x)) }$ and the other is $f(x)=f{\sqrt(x) }$.

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

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

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 $f(\sqrt{x})$.

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

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