derivative of ln(sin(7x))

解

\frac{d}{d x} (ln (sin (7 x)))

7 cot (7 x)

解答ステップ

\frac{d}{d x} (ln (sin (7 x)))

連鎖法則を適用:

\frac{1}{sin ( 7 x )} \frac{d}{d x} (sin (7 x))

= \frac{1}{sin ( 7 x )} \frac{d}{d x} (sin (7 x))

\frac{d}{d x} (sin (7 x)) = cos (7 x) \cdot 7

= \frac{1}{sin ( 7 x )} cos (7 x) \cdot 7

簡素化

\frac{1}{sin ( 7 x )} cos (7 x) \cdot 7 : 7 cot (7 x)

= 7 cot (7 x)