(\partial)/(\partial x)(ln(sin(x)))

解

\frac{\partial}{\partial x} (ln (sin (x)))

cot (x)

解答ステップ

\frac{\partial}{\partial x} (ln (sin (x)))

連鎖法則を適用:

\frac{1}{sin ( x )} \frac{\partial}{\partial x} (sin (x))

= \frac{1}{sin ( x )} \frac{\partial}{\partial x} (sin (x))

\frac{\partial}{\partial x} (sin (x)) = cos (x)

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

簡素化

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

= cot (x)