derivative of y^2-2xy+6x

解

\frac{d}{d x} (y^{2} - 2 x y + 6 x)

2 y \frac{d y}{d x} - 2 (y + x \frac{d y}{d x}) + 6

解答ステップ

\frac{d}{d x} (y^{2} - 2 x y + 6 x)

和/差の法則を適用:

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

= \frac{d}{d x} (y^{2}) - \frac{d}{d x} (2 x y) + \frac{d}{d x} (6 x)

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

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

\frac{d}{d x} (6 x) = 6

= 2 y \frac{d y}{d x} - 2 (y + x \frac{d y}{d x}) + 6