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

解

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

2 x - 4

解答ステップ

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

簡素化

(x - 2)^{2} + (y - 2)^{2} : x^{2} - 4 x + y^{2} + 8 - 4 y

= \frac{\partial}{\partial x} (x^{2} - 4 x + y^{2} + 8 - 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} (4 x) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (8) - \frac{\partial}{\partial x} (4 y)

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

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

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

\frac{\partial}{\partial x} (8) = 0

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

= 2 x - 4 + 0 + 0 - 0

簡素化

= 2 x - 4