derivative of e^{-1/(x^4})

解答

\frac{d}{d x} (e^{- \frac{1}{x ^{4}}})

\frac{4 e ^{- \frac{1}{x ^{4}}}}{x ^{5}}

求解步骤

\frac{d}{d x} (e^{- \frac{1}{x ^{4}}})

使用连锁律:

e^{- \frac{1}{x ^{4}}} \frac{d}{d x} (- \frac{1}{x ^{4}})

= e^{- \frac{1}{x ^{4}}} \frac{d}{d x} (- \frac{1}{x ^{4}})

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

= e^{- \frac{1}{x ^{4}}} \frac{4}{x ^{5}}

分式相乘:

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

= \frac{4 e ^{- \frac{1}{x ^{4}}}}{x ^{5}}

\frac{d}{d x} ((sin (cos (2 x)))^{2})

\frac{d}{d t} (20 - 25 sin^{2} (t))

\int 3 sin (x) d x

\frac{\partial}{\partial x} (x^{y} + ln (z))

sec (x) \frac{d y}{d x} = e^{y + s i n (x)}