(\partial)/(\partial x)(xe^{(x^2-y)})

解

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

e^{x^{2} - y} + 2 e^{x^{2} - y} x^{2}

解答ステップ

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

y

を定数として扱う

積の法則を適用:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot e^{x^{2} - y} + e^{x^{2} - y} \cdot 2 xx

簡素化

1 \cdot e^{x^{2} - y} + e^{x^{2} - y} \cdot 2 xx : e^{x^{2} - y} + 2 e^{x^{2} - y} x^{2}

= e^{x^{2} - y} + 2 e^{x^{2} - y} x^{2}