(\partial)/(\partial x)(xe^{7xy})

解答

\frac{\partial}{\partial x} (x e^{7 x y})

e^{7 x y} + 7 e^{7 x y} x y

求解步骤

\frac{\partial}{\partial x} (x e^{7 x y})

将

y

视为常数

使用微分乘法定则:

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

f = x, g = e^{7 x y}

= \frac{\partial}{\partial x} (x) e^{7 x y} + \frac{\partial}{\partial x} (e^{7 x y}) x

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

\frac{\partial}{\partial x} (e^{7 x y}) = e^{7 x y} \cdot 7 y

= 1 \cdot e^{7 x y} + e^{7 x y} \cdot 7 y x

化简

= e^{7 x y} + 7 e^{7 x y} x y