derivative of x^2-xy+y^2

解

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

2 x - y - x \frac{d y}{d x} + 2 y \frac{d y}{d x}

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

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

簡素化

= 2 x - y - x \frac{d y}{d x} + 2 y \frac{d y}{d x}