<s>[INST] Stuck calculating the derivative of $f(x)=\log_{10}{\frac{x}{1+\sqrt{5-x^2}}}$. I have to calculate the derivative of this:
$$f(x)=\log_{10}{\frac{x}{1+\sqrt{5-x^2}}}$$
But I'm stuck. This is the point where I have arrived:
$$f'(x) = \frac{(1+\sqrt{5-x^2})(\sqrt{5-x^2})+x^2}{x(\ln 10)(1+\sqrt{5-x^2})(\sqrt{5-x^2})}$$
How can I simplify? I didn't include all the passages.
 [/INST] The first derivative is given by $$f'(x)= \left(  \left( 1+\sqrt {5-{x}^{2}} \right) ^{-1}+{\frac {{x}^{2}}{
 \left( 1+\sqrt {5-{x}^{2}} \right) ^{2}\sqrt {5-{x}^{2}}}} \right) 
 \left( 1+\sqrt {5-{x}^{2}} \right) {x}^{-1} \left( \ln  \left( 10
 \right)  \right) ^{-1}
$$ and can be simplified to
$$f'(x)={\frac {\sqrt {5-{x}^{2}}+5}{x\ln  \left( 10 \right)  \left( 1+\sqrt {
5-{x}^{2}} \right) \sqrt {5-{x}^{2}}}}
$$
</s>