derivative of e^{sqrt(tan(3x)})

解

\frac{d}{d x} (e^{t a n (3 x)})

\frac{3 e ^{t a n (3 x)} sec ^{2} ( 3 x )}{2 tan ( 3 x )}

解答ステップ

\frac{d}{d x} (e^{t a n (3 x)})

連鎖法則を適用:

e^{t a n (3 x)} \frac{d}{d x} (tan (3 x))

= e^{t a n (3 x)} \frac{d}{d x} (tan (3 x))

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

= e^{t a n (3 x)} \frac{3 sec ^{2} ( 3 x )}{2 tan ( 3 x )}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 e ^{t a n (3 x)} sec ^{2} ( 3 x )}{2 tan ( 3 x )}