(\partial)/(\partial x)(4yx^3-12y^2x^2)

解答

\frac{\partial}{\partial x} (4 y x^{3} - 12 y^{2} x^{2})

12 y x^{2} - 24 y^{2} x

求解步骤

\frac{\partial}{\partial x} (4 y x^{3} - 12 y^{2} x^{2})

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} (4 y x^{3}) - \frac{\partial}{\partial x} (12 y^{2} x^{2})

\frac{\partial}{\partial x} (4 y x^{3}) = 12 y x^{2}

\frac{\partial}{\partial x} (12 y^{2} x^{2}) = 24 y^{2} x

= 12 y x^{2} - 24 y^{2} x

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