(\partial)/(\partial x)(12xy-x^3-y^3-7)

解答

\frac{\partial}{\partial x} (12 x y - x^{3} - y^{3} - 7)

12 y - 3 x^{2}

求解步骤

\frac{\partial}{\partial x} (12 x y - x^{3} - y^{3} - 7)

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} (12 x y) - \frac{\partial}{\partial x} (x^{3}) - \frac{\partial}{\partial x} (y^{3}) - \frac{\partial}{\partial x} (7)

\frac{\partial}{\partial x} (12 x y) = 12 y

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

\frac{\partial}{\partial x} (y^{3}) = 0

\frac{\partial}{\partial x} (7) = 0

= 12 y - 3 x^{2} - 0 - 0

化简

= 12 y - 3 x^{2}

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