derivative 3\sqrt[3]{x^2}

解

導関数

3 3 x^{2}

\frac{2 x}{( x ^{2} ) ^{\frac{2}{3}}}

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

= 3 \cdot \frac{1}{3 ( x ^{2} ) ^{\frac{2}{3}}} \cdot 2 x

簡素化

3 \cdot \frac{1}{3 ( x ^{2} ) ^{\frac{2}{3}}} \cdot 2 x : \frac{2 x}{( x ^{2} ) ^{\frac{2}{3}}}

= \frac{2 x}{( x ^{2} ) ^{\frac{2}{3}}}