derivative of 10sqrt(0.6x+7)

解

\frac{d}{d x} (10 0.6 x + 7)

\frac{3}{0.6 x + 7}

解答ステップ

\frac{d}{d x} (10 0.6 x + 7)

定数を除去:

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

= 10 \frac{d}{d x} (0.6 x + 7)

連鎖法則を適用:

\frac{1}{2 0.6 x + 7} \frac{d}{d x} (0.6 x + 7)

= \frac{1}{2 0.6 x + 7} \frac{d}{d x} (0.6 x + 7)

\frac{d}{d x} (0.6 x + 7) = 0.6

= 10 \cdot \frac{1}{2 0.6 x + 7} \cdot 0.6

簡素化

10 \cdot \frac{1}{2 0.6 x + 7} \cdot 0.6 : \frac{3}{0.6 x + 7}

= \frac{3}{0.6 x + 7}