(\partial)/(\partial y)(e^{yx}y^2)

解

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

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

解答ステップ

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

x

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

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

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

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

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