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

解答

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

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

求解步骤

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

将

y

视为常数

使用微分乘法定则:

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

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

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

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

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

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

化简

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

\frac{d}{d x} (arcsech (1 - x^{2}))

\frac{d}{d x} (x \cdot e^{x y})

\frac{d}{d x} ((cos^{2} (x))^{x})

x \to 0 - lim (x^{3} + 3 x + 2)

e^{x} y \cdot \frac{d y}{d x} = e^{- y} + e^{- 3 x - y}