derivative y=2x^2sqrt(2-x)

解

導関数

y = 2 x^{2} 2 - x

\frac{- 5 x ^{2} + 8 x}{2 - x}

解答ステップ

\frac{d}{d x} (2 x^{2} 2 - x)

定数を除去:

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

= 2 \frac{d}{d x} (x^{2} 2 - x)

積の法則を適用:

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

f = x^{2}, g = 2 - x

= 2 (\frac{d}{d x} (x^{2}) 2 - x + \frac{d}{d x} (2 - x) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

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

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

簡素化

2 (2 x 2 - x + (- \frac{1}{2 2 - x}) x^{2}) : \frac{- 5 x ^{2} + 8 x}{2 - x}

= \frac{- 5 x ^{2} + 8 x}{2 - x}