derivative of e^{(-1/(x^2)})

解答

\frac{d}{d x} (e^{\frac{- 1}{x ^{2}}})

\frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{3}}

求解步骤

\frac{d}{d x} (e^{\frac{- 1}{x ^{2}}})

化简

e^{\frac{- 1}{x ^{2}}} : e^{- \frac{1}{x ^{2}}}

= \frac{d}{d x} (e^{- \frac{1}{x ^{2}}})

使用连锁律:

e^{- \frac{1}{x ^{2}}} \frac{d}{d x} (- \frac{1}{x ^{2}})

= e^{- \frac{1}{x ^{2}}} \frac{d}{d x} (- \frac{1}{x ^{2}})

\frac{d}{d x} (- \frac{1}{x ^{2}}) = \frac{2}{x ^{3}}

= e^{- \frac{1}{x ^{2}}} \frac{2}{x ^{3}}

分式相乘:

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

= \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{3}}

x \to 3 lim (\frac{7 x ^{2} - 3 x}{x})

\frac{1}{4} (\frac{d y}{d t}) + 10 y = 5

\int sec^{2} (x t a) n^{2} x d x

t an g e n t f (x) = x^{3} - \frac{3}{2} x^{2} + x, at x = 1

n = 2 \sum \infty \frac{( - 1 ) ^{n}}{n ln ( n )}