derivative arcsec(1/(4t^5))

解答

导数

arcsec (\frac{1}{4 t ^{5}})

- \frac{20 t ^{4}}{1 - 16 t ^{10}}

求解步骤

\frac{d}{d t} (arcsec (\frac{1}{4 t ^{5}}))

使用连锁律:

\frac{1}{( \frac{1}{4 t ^{5}} ) ^{2} ( \frac{1}{4 t ^{5}} ) ^{2} - 1} \frac{d}{d t} (\frac{1}{4 t ^{5}})

= \frac{1}{( \frac{1}{4 t ^{5}} ) ^{2} ( \frac{1}{4 t ^{5}} ) ^{2} - 1} \frac{d}{d t} (\frac{1}{4 t ^{5}})

\frac{d}{d t} (\frac{1}{4 t ^{5}}) = - \frac{5}{4 t ^{6}}

= \frac{1}{( \frac{1}{4 t ^{5}} ) ^{2} ( \frac{1}{4 t ^{5}} ) ^{2} - 1} (- \frac{5}{4 t ^{6}})

化简

\frac{1}{( \frac{1}{4 t ^{5}} ) ^{2} ( \frac{1}{4 t ^{5}} ) ^{2} - 1} (- \frac{5}{4 t ^{6}}) : - \frac{20 t ^{4}}{1 - 16 t ^{10}}

= - \frac{20 t ^{4}}{1 - 16 t ^{10}}

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