derivative f(x)=(4x-3)(sqrt(x)+2)

解

導関数

f (x) = (4 x - 3) (x + 2)

\frac{12 x - 3}{2 x} + 8

解答ステップ

\frac{d}{d x} ((4 x - 3) (x + 2))

積の法則を適用:

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

f = 4 x - 3, g = x + 2

= \frac{d}{d x} (4 x - 3) (x + 2) + \frac{d}{d x} (x + 2) (4 x - 3)

\frac{d}{d x} (4 x - 3) = 4

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

= 4 (x + 2) + \frac{1}{2 x} (4 x - 3)

簡素化

4 (x + 2) + \frac{1}{2 x} (4 x - 3) : \frac{12 x - 3}{2 x} + 8

= \frac{12 x - 3}{2 x} + 8