derivative of x*sqrt(9-x)

解

\frac{d}{d x} (x \cdot 9 - x)

\frac{- 3 x + 18}{2 9 - x}

解答ステップ

\frac{d}{d x} (x 9 - x)

積の法則を適用:

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

f = x, g = 9 - x

= \frac{d x}{d x} 9 - x + \frac{d}{d x} (9 - x) x

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

\frac{d}{d x} (9 - x) = - \frac{1}{2 9 - x}

= 1 \cdot 9 - x + (- \frac{1}{2 9 - x}) x

簡素化

1 \cdot 9 - x + (- \frac{1}{2 9 - x}) x : \frac{- 3 x + 18}{2 9 - x}

= \frac{- 3 x + 18}{2 9 - x}