derivative of 3x^3y-y^3

解答

\frac{d}{d x} (3 x^{3} y - y^{3})

3 (3 x^{2} y + \frac{d y}{d x} x^{3}) - 3 y^{2} \frac{d y}{d x}

求解步骤

\frac{d}{d x} (3 x^{3} y - y^{3})

使用微分加减法定则:

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

= \frac{d}{d x} (3 x^{3} y) - \frac{d}{d x} (y^{3})

\frac{d}{d x} (3 x^{3} y) = 3 (3 x^{2} y + \frac{d y}{d x} x^{3})

\frac{d}{d x} (y^{3}) = 3 y^{2} \frac{d y}{d x}

= 3 (3 x^{2} y + \frac{d y}{d x} x^{3}) - 3 y^{2} \frac{d y}{d x}

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