(\partial)/(\partial x)((x+1)^2+2(y-1)^2)

解

\frac{\partial}{\partial x} ((x + 1)^{2} + 2 (y - 1)^{2})

2 x + 2

解答ステップ

\frac{\partial}{\partial x} ((x + 1)^{2} + 2 (y - 1)^{2})

簡素化

(x + 1)^{2} + 2 (y - 1)^{2} : x^{2} + 2 x + 2 y^{2} + 3 - 4 y

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

y

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

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

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

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

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

\frac{\partial}{\partial x} (4 y) = 0

= 2 x + 2 + 0 + 0 - 0

簡素化

= 2 x + 2