derivative of 2x^2+y^3

解答

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

4 x + 3 y^{2} \frac{d y}{d x}

求解步骤

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

使用微分加减法定则:

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

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

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

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

= 4 x + 3 y^{2} \frac{d y}{d x}

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