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人気のある微分積分 >

derivative of ln(cosh(x))

解

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

解

tanh (x)

解答ステップ

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

連鎖法則を適用:

\frac{1}{cosh ( x )} \frac{d}{d x} (cosh (x))

= \frac{1}{cosh ( x )} \frac{d}{d x} (cosh (x))

\frac{d}{d x} (cosh (x)) = sinh (x)

= \frac{1}{cosh ( x )} sinh (x)

簡素化

\frac{1}{cosh ( x )} sinh (x) : tanh (x)

= tanh (x)

グラフ

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