derivative of (3x-2y^2-(2x-3y)^2)

解

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

10 x - 10 y \frac{d y}{d x}

解答ステップ

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

簡素化

(3 x - 2 y)^{2} - (2 x - 3 y)^{2} : 5 x^{2} - 5 y^{2}

= \frac{d}{d x} (5 x^{2} - 5 y^{2})

和/差の法則を適用:

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

= \frac{d}{d x} (5 x^{2}) - \frac{d}{d x} (5 y^{2})

\frac{d}{d x} (5 x^{2}) = 10 x

\frac{d}{d x} (5 y^{2}) = 10 y \frac{d y}{d x}

= 10 x - 10 y \frac{d y}{d x}