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

解

導関数

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

\frac{9 x - 2}{2 x}

解答ステップ

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

積の法則を適用:

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

f = x, g = 3 x - 2

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

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

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

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

簡素化

\frac{1}{2 x} (3 x - 2) + 3 x : \frac{9 x - 2}{2 x}

= \frac{9 x - 2}{2 x}