derivative of 3sqrt(x-2)

解

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

\frac{3}{2 x - 2}

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{3}{2 x - 2}