derivative of 800sqrt(x^2-0.1x)

解

\frac{d}{d x} (800 x^{2} - 0.1 x)

\frac{400 ( 2 x - 0.1 )}{x ^{2} - 0.1 x}

解答ステップ

\frac{d}{d x} (800 x^{2} - 0.1 x)

定数を除去:

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

= 800 \frac{d}{d x} (x^{2} - 0.1 x)

連鎖法則を適用:

\frac{1}{2 x ^{2} - 0.1 x} \frac{d}{d x} (x^{2} - 0.1 x)

= \frac{1}{2 x ^{2} - 0.1 x} \frac{d}{d x} (x^{2} - 0.1 x)

\frac{d}{d x} (x^{2} - 0.1 x) = 2 x - 0.1

= 800 \cdot \frac{1}{2 x ^{2} - 0.1 x} (2 x - 0.1)

簡素化

800 \cdot \frac{1}{2 x ^{2} - 0.1 x} (2 x - 0.1) : \frac{400 ( 2 x - 0.1 )}{x ^{2} - 0.1 x}

= \frac{400 ( 2 x - 0.1 )}{x ^{2} - 0.1 x}