derivative of tan^2(sqrt(x))

解

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

\frac{sec ^{2} ( x ) tan ( x )}{x}

解答ステップ

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

連鎖法則を適用:

2 tan (x) \frac{d}{d x} (tan (x))

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

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

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

簡素化

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

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