(\partial)/(\partial y)(sin(xy^2+y)+2e^x)

解

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

cos (x y^{2} + y) (2 x y + 1)

解答ステップ

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

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

\frac{\partial}{\partial y} (sin (x y^{2} + y)) = cos (x y^{2} + y) (2 x y + 1)

\frac{\partial}{\partial y} (2 e^{x}) = 0

= cos (x y^{2} + y) (2 x y + 1) + 0

簡素化

= cos (x y^{2} + y) (2 x y + 1)