d/(dt)(tan(sqrt(5t)))

解

\frac{d}{d t} (tan (5 t))

\frac{5 sec ^{2} ( 5 t )}{2 t}

解答ステップ

\frac{d}{d t} (tan (5 t))

簡素化

tan (5 t) : tan (5 t)

= \frac{d}{d t} (tan (5 t))

連鎖法則を適用:

sec^{2} (5 t) \frac{d}{d t} (5 t)

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

\frac{d}{d t} (5 t) = \frac{5}{2 t}

= sec^{2} (5 t) \frac{5}{2 t}

分数を乗じる:

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

= \frac{5 sec ^{2} ( 5 t )}{2 t}