derivative of 30x^4y^7-24x^{12}y^3

解

\frac{d}{d x} (30 x^{4} y^{7} - 24 x^{12} y^{3})

30 (4 x^{3} y^{7} + 7 y^{6} \frac{d y}{d x} x^{4}) - 24 (12 x^{11} y^{3} + 3 y^{2} \frac{d y}{d x} x^{12})

解答ステップ

\frac{d}{d x} (30 x^{4} y^{7} - 24 x^{12} y^{3})

和/差の法則を適用:

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

= \frac{d}{d x} (30 x^{4} y^{7}) - \frac{d}{d x} (24 x^{12} y^{3})

\frac{d}{d x} (30 x^{4} y^{7}) = 30 (4 x^{3} y^{7} + 7 y^{6} \frac{d y}{d x} x^{4})

\frac{d}{d x} (24 x^{12} y^{3}) = 24 (12 x^{11} y^{3} + 3 y^{2} \frac{d y}{d x} x^{12})

= 30 (4 x^{3} y^{7} + 7 y^{6} \frac{d y}{d x} x^{4}) - 24 (12 x^{11} y^{3} + 3 y^{2} \frac{d y}{d x} x^{12})