derivative f(x)=1100(sqrt(x^2-0.2x))

解

導関数

f (x) = 1100 (x^{2} - 0.2 x)

\frac{550 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

解答ステップ

\frac{d}{d x} (1100 x^{2} - 0.2 x)

定数を除去:

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

= 1100 \frac{d}{d x} (x^{2} - 0.2 x)

連鎖法則を適用:

\frac{1}{2 x ^{2} - 0.2 x} \frac{d}{d x} (x^{2} - 0.2 x)

= \frac{1}{2 x ^{2} - 0.2 x} \frac{d}{d x} (x^{2} - 0.2 x)

\frac{d}{d x} (x^{2} - 0.2 x) = 2 x - 0.2

= 1100 \cdot \frac{1}{2 x ^{2} - 0.2 x} (2 x - 0.2)

簡素化

1100 \cdot \frac{1}{2 x ^{2} - 0.2 x} (2 x - 0.2) : \frac{550 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

= \frac{550 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}