(xsqrt(1-x^2))^'

解

(x 1 - x^{2})^{^{'}}

\frac{- 2 x ^{2} + 1}{1 - x ^{2}}

解答ステップ

(x 1 - x^{2})^{'}

積の法則を適用:

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

f = x, g = 1 - x^{2}

= x^{^{'}} 1 - x^{2} + (1 - x^{2})^{^{'}} x

x^{'} = 1

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

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

簡素化

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

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