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

解

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

4 x^{3} - 4 x

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} - a - 1, g = x^{2} + a - 1

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

\frac{\partial}{\partial x} (x^{2} - a - 1) = 2 x

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

= 2 x (x^{2} + a - 1) + 2 x (x^{2} - a - 1)

簡素化

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

= 4 x^{3} - 4 x