(\partial)/(\partial x)(xye^{x-2z})

解答

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

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

求解步骤

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

将

y, z

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分乘法定则:

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

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

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

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

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

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

化简

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

\frac{\partial}{\partial x} (A + B \cdot cos (x) sin (y))

\frac{d x}{d t} = x^{\frac{2}{3}}

in v erse l a pl a ce \frac{1}{4 s ^{2}}

y^{^{'}} - y = 3 t e^{2 t}, y (0) = 1

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