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

解

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

4 x + 2 y + 2

解答ステップ

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

簡素化

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

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

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

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

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

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

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

\frac{\partial}{\partial x} (1) = 0

= 4 x + 2 y + 2 + 0 + 0

簡素化

= 4 x + 2 y + 2