(\partial)/(\partial x)(e^{-2x^2-y^2})

解答

\frac{\partial}{\partial x} (e^{- 2 x^{2} - y^{2}})

- 4 e^{- 2 x^{2} - y^{2}} x

求解步骤

\frac{\partial}{\partial x} (e^{- 2 x^{2} - y^{2}})

将

y

视为常数

使用连锁律:

e^{- 2 x^{2} - y^{2}} \frac{\partial}{\partial x} (- 2 x^{2} - y^{2})

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

\frac{\partial}{\partial x} (- 2 x^{2} - y^{2}) = - 4 x

= e^{- 2 x^{2} - y^{2}} (- 4 x)

化简

= - 4 e^{- 2 x^{2} - y^{2}} x

\int - e^{x} sin (y) d y

\frac{\partial}{\partial y} (x + 2 y + z)

\int x^{2} e^{- 1} d x

\int \frac{( x ^{2} - 4 x + 9 )}{x ^{2} - 6 x + 9} d x

in v erse l a pl a ce \frac{( 3 s + 7 )}{s ^{2} + 2 s + 4}