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:

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

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

Then chain rule:

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

and my answer is:

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

How can I simplify this? >implying its correct