Answer
$f'(x)=\pi$$x^{\pi-1}-\frac{\sqrt {10}}{x^{(1+\sqrt {10})}}$
Work Step by Step
$f(x)=x^{\pi}+\frac{1}{x^{\sqrt {10}}}=x^{\pi}+x^{-\sqrt {10}}$
$f'(x)=\pi$$x^{\pi-1}-\sqrt {10}x^{-\sqrt {10}-1}$
$f'(x)=\pi$$x^{\pi-1}-\frac{\sqrt {10}}{x^{(1+\sqrt {10})}}$