(\partial)/(\partial x)(54-2/3 x^2-4y^2)

解答

\frac{\partial}{\partial x} (54 - \frac{2}{3} x^{2} - 4 y^{2})

- \frac{4 x}{3}

求解步骤

\frac{\partial}{\partial x} (54 - \frac{2}{3} x^{2} - 4 y^{2})

化简

54 - \frac{2}{3} x^{2} - 4 y^{2} : 54 - \frac{2 x ^{2}}{3} - 4 y^{2}

= \frac{\partial}{\partial x} (54 - \frac{2 x ^{2}}{3} - 4 y^{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} (54) - \frac{\partial}{\partial x} (\frac{2 x ^{2}}{3}) - \frac{\partial}{\partial x} (4 y^{2})

\frac{\partial}{\partial x} (54) = 0

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

\frac{\partial}{\partial x} (4 y^{2}) = 0

= 0 - \frac{4 x}{3} - 0

化简

= - \frac{4 x}{3}

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