derivative of 3x^3y-2x^2y^2+3y

解

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

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

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

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