(\partial)/(\partial x)((x-4)^2+(y-4)^2-5)

解

\frac{\partial}{\partial x} ((x - 4)^{2} + (y - 4)^{2} - 5)

2 x - 8

解答ステップ

\frac{\partial}{\partial x} ((x - 4)^{2} + (y - 4)^{2} - 5)

簡素化

(x - 4)^{2} + (y - 4)^{2} - 5 : x^{2} - 8 x + y^{2} + 27 - 8 y

= \frac{\partial}{\partial x} (x^{2} - 8 x + y^{2} + 27 - 8 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} (8 x) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (27) - \frac{\partial}{\partial x} (8 y)

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

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

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

\frac{\partial}{\partial x} (27) = 0

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

= 2 x - 8 + 0 + 0 - 0

簡素化

= 2 x - 8