derivative f(x)=3(sqrt(x+1))

解

導関数

f (x) = 3 (x + 1)

\frac{3}{2 x + 1}

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

= 3 \cdot \frac{1}{2 x + 1} \cdot 1

簡素化

3 \cdot \frac{1}{2 x + 1} \cdot 1 : \frac{3}{2 x + 1}

= \frac{3}{2 x + 1}