derivative of (a-xsqrt(a+x))

解

\frac{d}{d x} ((a - x) a + x)

\frac{- 3 x - a}{2 a + x}

解答ステップ

\frac{d}{d x} ((a - x) a + x)

積の法則を適用:

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

f = a - x, g = a + x

= \frac{d}{d x} (a - x) a + x + \frac{d}{d x} (a + x) (a - x)

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

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

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

簡素化

(- 1) a + x + \frac{1}{2 a + x} (a - x) : \frac{- 3 x - a}{2 a + x}

= \frac{- 3 x - a}{2 a + x}