(\partial)/(\partial y)(y^2sin(xy))

解

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

2 y sin (x y) + cos (x y) x y^{2}

解答ステップ

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

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 = y^{2}, g = sin (x y)

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

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

\frac{\partial}{\partial y} (sin (x y)) = cos (x y) x

= 2 y sin (x y) + cos (x y) x y^{2}