(\partial)/(\partial y)(3x^2y+cos(y))

解

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

3 x^{2} - sin (y)

解答ステップ

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

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

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

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