derivative of \sqrt[3]{{g}(x})

解

\frac{d}{d x} (3 g (x))

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

解答ステップ

\frac{d}{d x} (3 g (x))

連鎖法則を適用:

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

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

簡素化

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

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