((x-sqrt(x))*(x+sqrt(x)))^'

解

((x - x) \cdot (x + x))^{^{'}}

2 x - 1

解答ステップ

((x - x) (x + x))^{'}

積の法則を適用:

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

f = x - x, g = x + x

= (x - x)^{^{'}} (x + x) + (x + x)^{^{'}} (x - x)

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

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

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

簡素化

(1 - \frac{1}{2 x}) (x + x) + (1 + \frac{1}{2 x}) (x - x) : 2 x - 1

= 2 x - 1