Найдите производную функции: f(x)=1/4*x^-10.

Ответ:

\[f(x) = \frac{1}{4}x^{- 10} = \frac{1}{4x^{10}}.\]

\[f'(x) = - \frac{\left( \frac{1}{4} \cdot 10x^{9} \right)}{\left( x^{10} \right)^{2}} =\]

\[= - \frac{\frac{5}{2}x^{9}}{x^{20}} = - \frac{5}{2x^{11}}.\]