derivative of e^{-(x^2+y^2})

解答

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

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

求解步骤

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

化简

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

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

使用连锁律:

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

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

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

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

t an g e n t y sin (8 x) = x cos (2 y), (\frac{π}{2}, \frac{π}{4})

\frac{d}{d x} (5 sec (2 x))

\int y ln (y) d y

im pl i c i t \frac{d y}{d x}, e^{2 x} sin (3 x) - e^{- 2 x} sin (2 y) = 13 x y^{2}

d er i v a t i v e cos (x) + sin (x)