derivative of xe^{x^2-y}

解

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

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

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x^{2} - y}

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x^{2} - y} + e^{x^{2} - y} (2 x - \frac{d y}{d x}) x

簡素化

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