derivative f(x)=(12-x)sqrt(24x-144)

解

導関数

f (x) = (12 - x) 24 x - 144

\frac{- 36 x + 288}{24 x - 144}

解答ステップ

\frac{d}{d x} ((12 - x) 24 x - 144)

積の法則を適用:

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

f = 12 - x, g = 24 x - 144

= \frac{d}{d x} (12 - x) 24 x - 144 + \frac{d}{d x} (24 x - 144) (12 - x)

\frac{d}{d x} (12 - x) = - 1

\frac{d}{d x} (24 x - 144) = \frac{12}{24 x - 144}

= (- 1) 24 x - 144 + \frac{12}{24 x - 144} (12 - x)

簡素化

(- 1) 24 x - 144 + \frac{12}{24 x - 144} (12 - x) : \frac{- 36 x + 288}{24 x - 144}

= \frac{- 36 x + 288}{24 x - 144}