(\partial)/(\partial x)(x^3y^2-2xe^{xy})

解

\frac{\partial}{\partial x} (x^{3} y^{2} - 2 x e^{x y})

3 y^{2} x^{2} - 2 (e^{y x} + y e^{y x} x)

解答ステップ

\frac{\partial}{\partial x} (x^{3} y^{2} - 2 x e^{x y})

y

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 x} (x^{3} y^{2}) - \frac{\partial}{\partial x} (2 x e^{x y})

\frac{\partial}{\partial x} (x^{3} y^{2}) = 3 y^{2} x^{2}

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

= 3 y^{2} x^{2} - 2 (e^{y x} + y e^{y x} x)