(\partial)/(\partial x)(x^2y^2-3y)

解

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

2 x y^{2}

解答ステップ

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

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

\frac{\partial}{\partial x} (3 y) = 0

= 2 y^{2} x - 0

簡素化

= 2 x y^{2}