derivative of (0.25/(\sqrt[5]{x^2)})

解

\frac{d}{d x} (\frac{0.25}{5 x ^{2}})

- \frac{0.1}{x ^{\frac{7}{5}}}

解答ステップ

\frac{d}{d x} (\frac{0.25}{5 x ^{2}})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 0.25 \frac{d}{d x} (\frac{1}{5 x ^{2}})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= 0.25 \frac{d}{d x} ((x^{2})^{- \frac{1}{5}})

連鎖法則を適用:

- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

= - \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

\frac{d}{d x} (x^{2}) = 2 x

= 0.25 (- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x)

簡素化

0.25 (- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x) : - \frac{0.1}{x ^{\frac{7}{5}}}

= - \frac{0.1}{x ^{\frac{7}{5}}}