d/(d{x)}(e^{-({x}^2+{y}^2+{z}^2)})

解答

\frac{d}{d x} (e^{- (x^{2} + y^{2} + z^{2})})

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

求解步骤

\frac{d}{d x} (e^{- (x^{2} + y^{2} + z^{2})})

化简

e^{- (x^{2} + y^{2} + z^{2})} : e^{- x^{2} - y^{2} - z^{2}}

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

使用连锁律:

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

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

\frac{d}{d x} (- x^{2} - y^{2} - z^{2}) = - 2 x

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

化简

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