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

解答

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

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

求解步骤

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

将

x

视为常数

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = e^{- x^{2} + y}

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

\frac{\partial}{\partial y} (y) = 1

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

= 1 \cdot e^{- x^{2} + y} + e^{- x^{2} + y} y

化简

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

\int \frac{x ^{2} + 3}{x x ^{2} - 9} d x

\frac{\partial}{\partial x} (cos^{6} (x^{8} y^{6}))

a re a y = 2 x - x^{2}, y = 2 x - 4

x \to 9 lim \frac{( x ^{\frac{1}{2}} - 3 ) ( x + 1 )}{x ^{2} - 8 x - 9}

d er i v a t i v e y = (3 x^{2} - 2 x - 4) 5^{x}