# Derivative of logarithmic function.

• May 23rd 2013, 08:08 PM
camjerlams
Derivative of logarithmic function.
Hi guys I am working on a derivative problem and think I have the answer but my algebra with logs is embarrassing so I'm struggling to simplify my answer. Here it is:

$f(x)= \sqrt{\log_{5} x+1}-1$

So, $f'(x)= \frac{d}{dx}(\frac{\ln(x)}{\ln5}+1)^\frac{1}{2}+0$ (d/dx(-1)=0)

Then chain rule:

$\frac{1}{2}\times(\frac{\ln(x)}{\ln(5)}+1)^\frac{-1}{2}\times\frac{1}{x\ln(5)}$

$\frac{1}{2\times\sqrt{log_{5}x+1}}\times\frac{1}{x \ln(5)}$