(\partial)/(\partial x)((x+2)^2-2(y-1)^2-5)

解

\frac{\partial}{\partial x} ((x + 2)^{2} - 2 (y - 1)^{2} - 5)

2 x + 4

解答ステップ

\frac{\partial}{\partial x} ((x + 2)^{2} - 2 (y - 1)^{2} - 5)

簡素化

(x + 2)^{2} - 2 (y - 1)^{2} - 5 : x^{2} + 4 x + 4 y - 2 y^{2} - 3

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

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

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

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

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

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

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

= 2 x + 4 + 0 - 0 - 0

簡素化

= 2 x + 4