derivative of x/(4.5c(c-x))

解

\frac{d}{d x} (\frac{x}{4.5 c} (c - x))

\frac{c - 2 x}{4.5 c}

解答ステップ

\frac{d}{d x} (\frac{x}{4.5 c} (c - x))

定数を除去:

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

= \frac{1}{4.5 c} \frac{d}{d x} (x (c - x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = c - x

= \frac{1}{4.5 c} (\frac{d x}{d x} (c - x) + \frac{d}{d x} (c - x) x)

\frac{d x}{d x} = 1

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

= \frac{1}{4.5 c} (1 \cdot (c - x) + (- 1) x)

簡素化

\frac{1}{4.5 c} (1 \cdot (c - x) + (- 1) x) : \frac{c - 2 x}{4.5 c}

= \frac{c - 2 x}{4.5 c}