(\partial)/(\partial x)(cos(ln(x)))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

= - sin (ln (x)) \frac{1}{x}

簡素化

- sin (ln (x)) \frac{1}{x} : - \frac{sin ( ln ( x ) )}{x}

= - \frac{sin ( ln ( x ) )}{x}