# determine where f is differentiable..

• April 18th 2010, 12:23 PM
tn11631
determine where f is differentiable..
Define f(x)=sqrt(x+sqrt(x+sqrt(x))) for x >=0. Determine where f is differentiable and compute the derivative.
• April 18th 2010, 01:29 PM
southprkfan1
Quote:

Originally Posted by tn11631
Define f(x)=sqrt(x+sqrt(x+sqrt(x))) for x >=0. Determine where f is differentiable and compute the derivative.

Chain rule!

$f'(x) = \frac{1}{2(x+\sqrt{x+\sqrt{x}})^{1/2}}*[1+(\frac{1}{2(x+\sqrt{x})^{1/2}})*(1+\frac{1}{2x^{1/2}})]$

Odds are I screwed up somewhere