derivative ((17-x)sqrt(2x+8))/2

解

導関数

\frac{( 17 - x ) 2 x + 8}{2}

\frac{- 3 x + 9}{2 2 x + 8}

解答ステップ

\frac{d}{d x} (\frac{( 17 - x ) 2 x + 8}{2})

定数を除去:

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

= \frac{1}{2} \frac{d}{d x} ((17 - x) 2 x + 8)

積の法則を適用:

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

f = 17 - x, g = 2 x + 8

= \frac{1}{2} (\frac{d}{d x} (17 - x) 2 x + 8 + \frac{d}{d x} (2 x + 8) (17 - x))

\frac{d}{d x} (17 - x) = - 1

\frac{d}{d x} (2 x + 8) = \frac{1}{2 x + 8}

= \frac{1}{2} ((- 1) 2 x + 8 + \frac{1}{2 x + 8} (17 - x))

簡素化

\frac{1}{2} ((- 1) 2 x + 8 + \frac{1}{2 x + 8} (17 - x)) : \frac{- 3 x + 9}{2 2 x + 8}

= \frac{- 3 x + 9}{2 2 x + 8}