derivative of ln(cos(ln(x)))

解

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

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

解答ステップ

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

連鎖法則を適用:

\frac{1}{cos ( ln ( x ) )} \frac{d}{d x} (cos (ln (x)))

= \frac{1}{cos ( ln ( x ) )} \frac{d}{d x} (cos (ln (x)))

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

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

簡素化

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

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