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人気のある微分積分 >

derivative 2/(\sqrt[4]{16x^3)}

解

導関数

\frac{2}{4 16 x ^{3}}

解

- \frac{3 x ^{2}}{4 ( x ^{3} ) ^{\frac{5}{4}}}

解答ステップ

\frac{d}{d x} (\frac{2}{4 16 x ^{3}})

定数を除去:

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

= 2 \frac{d}{d x} (\frac{1}{4 16 x ^{3}})

指数の規則を適用する:

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

= 2 \frac{d}{d x} ((16 x^{3})^{- \frac{1}{4}})

連鎖法則を適用:

- \frac{1}{4 ( 16 x ^{3} ) ^{\frac{5}{4}}} \frac{d}{d x} (16 x^{3})

= - \frac{1}{4 ( 16 x ^{3} ) ^{\frac{5}{4}}} \frac{d}{d x} (16 x^{3})

\frac{d}{d x} (16 x^{3}) = 48 x^{2}

= 2 (- \frac{1}{4 ( 16 x ^{3} ) ^{\frac{5}{4}}} \cdot 48 x^{2})

簡素化

2 (- \frac{1}{4 ( 16 x ^{3} ) ^{\frac{5}{4}}} \cdot 48 x^{2}) : - \frac{3 x ^{2}}{4 ( x ^{3} ) ^{\frac{5}{4}}}

= - \frac{3 x ^{2}}{4 ( x ^{3} ) ^{\frac{5}{4}}}

グラフ

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