(\partial)/(\partial x)(2x^2-6y^3+3z^2)

解答

\frac{\partial}{\partial x} (2 x^{2} - 6 y^{3} + 3 z^{2})

4 x

求解步骤

\frac{\partial}{\partial x} (2 x^{2} - 6 y^{3} + 3 z^{2})

将

y, z

视为常数

使用微分加减法定则:

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

= \frac{\partial}{\partial x} (2 x^{2}) - \frac{\partial}{\partial x} (6 y^{3}) + \frac{\partial}{\partial x} (3 z^{2})

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

\frac{\partial}{\partial x} (6 y^{3}) = 0

\frac{\partial}{\partial x} (3 z^{2}) = 0

= 4 x - 0 + 0

化简

= 4 x

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