derivative e^{-5/(t^7)}

解答

导数

e^{- \frac{5}{t ^{7}}}

\frac{35 e ^{- \frac{5}{t ^{7}}}}{t ^{8}}

求解步骤

\frac{d}{d t} (e^{- \frac{5}{t ^{7}}})

使用连锁律:

e^{- \frac{5}{t ^{7}}} \frac{d}{d t} (- \frac{5}{t ^{7}})

= e^{- \frac{5}{t ^{7}}} \frac{d}{d t} (- \frac{5}{t ^{7}})

\frac{d}{d t} (- \frac{5}{t ^{7}}) = \frac{35}{t ^{8}}

= e^{- \frac{5}{t ^{7}}} \frac{35}{t ^{8}}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{35 e ^{- \frac{5}{t ^{7}}}}{t ^{8}}

\frac{d}{d x} (x^{- 2} (4 + 3 x^{- 3}))

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