(\partial)/(\partial y)(x^4y-3x^5y^2)

解答

\frac{\partial}{\partial y} (x^{4} y - 3 x^{5} y^{2})

x^{4} - 6 x^{5} y

求解步骤

\frac{\partial}{\partial y} (x^{4} y - 3 x^{5} y^{2})

将

x

视为常数

使用微分加减法定则:

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

= \frac{\partial}{\partial y} (x^{4} y) - \frac{\partial}{\partial y} (3 x^{5} y^{2})

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

\frac{\partial}{\partial y} (3 x^{5} y^{2}) = 6 x^{5} y

= x^{4} - 6 x^{5} y

x \to 1 lim (x + 1)

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