derivative y=arcsin(x)-sqrt(1-x^2)

解

導関数

y = arcsin (x) - 1 - x^{2}

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

解答ステップ

\frac{d}{d x} (arcsin (x) - 1 - x^{2})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

簡素化

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

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