(\partial)/(\partial x)(x^3e^{xy}+2y)

解答

\frac{\partial}{\partial x} (x^{3} e^{x y} + 2 y)

e^{x y} x^{3} y + 3 e^{x y} x^{2}

求解步骤

\frac{\partial}{\partial x} (x^{3} e^{x y} + 2 y)

将

y

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{3} e^{x y}) + \frac{\partial}{\partial x} (2 y)

\frac{\partial}{\partial x} (x^{3} e^{x y}) = 3 x^{2} e^{x y} + e^{x y} y x^{3}

\frac{\partial}{\partial x} (2 y) = 0

= 3 x^{2} e^{x y} + e^{x y} y x^{3} + 0

化简

= e^{x y} x^{3} y + 3 e^{x y} x^{2}

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