derivative of \sqrt[3]{1+tan(x})

解

\frac{d}{d x} (3 1 + tan (x))

\frac{sec ^{2} ( x )}{3 ( 1 + tan ( x ) ) ^{\frac{2}{3}}}

解答ステップ

\frac{d}{d x} (3 1 + tan (x))

連鎖法則を適用:

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

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

\frac{d}{d x} (1 + tan (x)) = sec^{2} (x)

= \frac{1}{3 ( 1 + tan ( x ) ) ^{\frac{2}{3}}} sec^{2} (x)

簡素化

\frac{1}{3 ( 1 + tan ( x ) ) ^{\frac{2}{3}}} sec^{2} (x) : \frac{sec ^{2} ( x )}{3 ( 1 + tan ( x ) ) ^{\frac{2}{3}}}

= \frac{sec ^{2} ( x )}{3 ( 1 + tan ( x ) ) ^{\frac{2}{3}}}