derivative-3xsqrt(x+1)

解

導関数

- 3 x x + 1

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

解答ステップ

\frac{d}{d x} (- 3 x x + 1)

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

積の法則を適用:

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

f = x, g = x + 1

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

\frac{d x}{d x} = 1

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

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

簡素化

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

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