(\partial)/(\partial y)(4x^3y^3-3x^2sin(x^3)y)

解

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 3 x^{2} sin (x^{3}) y)

12 x^{3} y^{2} - 3 x^{2} sin (x^{3})

解答ステップ

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 3 x^{2} sin (x^{3}) 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} (4 x^{3} y^{3}) - \frac{\partial}{\partial y} (3 x^{2} sin (x^{3}) y)

\frac{\partial}{\partial y} (4 x^{3} y^{3}) = 12 x^{3} y^{2}

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

= 12 x^{3} y^{2} - 3 x^{2} sin (x^{3})