derivative of tan(sin(sqrt(5x)))

解

\frac{d}{d x} (tan (sin (5 x)))

\frac{5 sec ^{2} ( sin ( 5 x ) ) cos ( 5 x )}{2 x}

解答ステップ

\frac{d}{d x} (tan (sin (5 x)))

簡素化

tan (sin (5 x)) : tan (sin (5 x))

= \frac{d}{d x} (tan (sin (5 x)))

連鎖法則を適用:

sec^{2} (sin (5 x)) \frac{d}{d x} (sin (5 x))

= sec^{2} (sin (5 x)) \frac{d}{d x} (sin (5 x))

\frac{d}{d x} (sin (5 x)) = \frac{5 cos ( 5 x )}{2 x}

= sec^{2} (sin (5 x)) \frac{5 cos ( 5 x )}{2 x}

分数を乗じる:

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

= \frac{5 sec ^{2} ( sin ( 5 x ) ) cos ( 5 x )}{2 x}