(\partial)/(\partial x)(x^4+y^4-4xy+2)

解答

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

4 x^{3} - 4 y

求解步骤

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

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

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

\frac{\partial}{\partial x} (4 x y) = 4 y

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

= 4 x^{3} + 0 - 4 y + 0

化简

= 4 x^{3} - 4 y