(\partial)/(\partial x)(e^{-1/x})

解答

\frac{\partial}{\partial x} (e^{- \frac{1}{x}})

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

求解步骤

\frac{\partial}{\partial x} (e^{- \frac{1}{x}})

使用连锁律:

e^{- \frac{1}{x}} \frac{\partial}{\partial x} (- \frac{1}{x})

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

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

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

化简

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

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

- 3 x^{2} y + y^{^{'}} = - 9 x^{2}

\int_{- 8}^{0} 2 + 64 - x^{2} d x

t an g e n t y = \frac{2}{x - 2}, (4, 1)

\frac{d}{d t} (t^{2} + t)

d er i v a t i v e y = \frac{- 12}{3 x}