(\partial)/(\partial x)(xy+yz^2+xz^3)

解答

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

y + z^{3}

求解步骤

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

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

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

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

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

= y + 0 + z^{3}

化简

= y + z^{3}

\frac{\partial}{\partial x} ((x + z) e^{x - y})

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