Question

Найдите y' (32), если y={x}^{-\frac{1}{5}}+{x}^{\frac{1}{5}}+x .

Выберите один ответ:
1\dfrac{3}{\text{64}}
1\dfrac{3}{\text{320}}
\dfrac{1}{\text{10}}
-\dfrac{3}{\text{320}}

Answer 1

$y=x^{-\frac{1}{5}}+x^{\frac{1}{5}}+x\\\\y'=-\frac{1}{5}\, x^{-\frac{6}{5}}+\frac{1}{5}\, x^{-\frac{4}{5}}+1=-\frac{1}{5\sqrt[5]{x^6}}+\frac{1}{5\sqrt[5]{x^4}}+1\\\\y'(32)=-\frac{1}{5\sqrt[5]{32^6}}+\frac{1}{5\sqrt[5]{32^4}}+1=-\frac{1}{5\cdot 2^6}+\frac{1}{5\cdot 2^4}+1=\frac{-1+2^2+5\cdot 2^6}{5\cdot 2^6}=\\\\=\frac{-1+4+320}{5\cdot 2^6}=\frac{323}{320}=1\frac{3}{320}$