(\partial)/(\partial x)((y)(x^2+6xy+y^3))

解

\frac{\partial}{\partial x} ((y) (x^{2} + 6 x y + y^{3}))

y (6 y + 2 x)

解答ステップ

\frac{\partial}{\partial x} ((y) (x^{2} + 6 x y + y^{3}))

y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (x^{2} + 6 x y + y^{3})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= y (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (6 x y) + \frac{\partial}{\partial x} (y^{3}))

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

\frac{\partial}{\partial x} (6 x y) = 6 y

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

= y (2 x + 6 y + 0)

簡素化

= y (6 y + 2 x)