derivative (x-sqrt(x))(x+sqrt(x))

解

導関数

(x - x) (x + x)

2 x - 1

解答ステップ

\frac{d}{d x} ((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

= \frac{d}{d x} (x - x) (x + x) + \frac{d}{d x} (x + x) (x - x)

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

\frac{d}{d 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