derivative of sech(ln(x^2))

解

\frac{d}{d x} (sech (ln (x^{2})))

- \frac{2 sech ( 2 ln ( x ) ) tanh ( 2 ln ( x ) )}{x}

解答ステップ

\frac{d}{d x} (sech (ln (x^{2})))

連鎖法則を適用:

- sech (ln (x^{2})) tanh (ln (x^{2})) \frac{d}{d x} (ln (x^{2}))

= - sech (ln (x^{2})) tanh (ln (x^{2})) \frac{d}{d x} (ln (x^{2}))

\frac{d}{d x} (ln (x^{2})) = \frac{2}{x}

= - sech (ln (x^{2})) tanh (ln (x^{2})) \frac{2}{x}

簡素化

- sech (ln (x^{2})) tanh (ln (x^{2})) \frac{2}{x} : - \frac{2 sech ( 2 ln ( x ) ) tanh ( 2 ln ( x ) )}{x}

= - \frac{2 sech ( 2 ln ( x ) ) tanh ( 2 ln ( x ) )}{x}