derivative of e^{ktan(sqrt(7x)})

解

\frac{d}{d x} (e^{k t a n (7 x)})

\frac{7 k e ^{k t a n (7 x)} sec ^{2} ( 7 x )}{2 x}

解答ステップ

\frac{d}{d x} (e^{k t a n (7 x)})

簡素化

e^{k t a n (7 x)} : e^{k t a n (7 x)}

= \frac{d}{d x} (e^{k t a n (7 x)})

連鎖法則を適用:

e^{k t a n (7 x)} \frac{d}{d x} (k tan (7 x))

= e^{k t a n (7 x)} \frac{d}{d x} (k tan (7 x))

\frac{d}{d x} (k tan (7 x)) = \frac{7 k sec ^{2} ( 7 x )}{2 x}

= e^{k t a n (7 x)} \frac{7 k sec ^{2} ( 7 x )}{2 x}

分数を乗じる:

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

= \frac{7 k e ^{k t a n (7 x)} sec ^{2} ( 7 x )}{2 x}