derivative of \sqrt[5]{ln(x})

解答

\frac{d}{d x} (5 ln (x))

\frac{1}{5 x ln ^{\frac{4}{5}} ( x )}

求解步骤

\frac{d}{d x} (5 ln (x))

使用连锁律:

\frac{1}{5 ( ln ( x ) ) ^{\frac{4}{5}}} \frac{d}{d x} (ln (x))

= \frac{1}{5 ( ln ( x ) ) ^{\frac{4}{5}}} \frac{d}{d x} (ln (x))

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

= \frac{1}{5 ( ln ( x ) ) ^{\frac{4}{5}}} \cdot \frac{1}{x}

化简

\frac{1}{5 ln ^{\frac{4}{5}} ( x )} \cdot \frac{1}{x} : \frac{1}{5 x ln ^{\frac{4}{5}} ( x )}

= \frac{1}{5 x ln ^{\frac{4}{5}} ( x )}

\frac{d}{d x} (3 sin (x) + 2 cos (x) tan (x))

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