(\partial)/(\partial y)(x^2+e^{xy})

解

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

e^{x y} x

解答ステップ

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

x

を定数として扱う

和/差の法則を適用:

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

= 0 + e^{x y} x

簡素化

= e^{x y} x