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

解

導関数

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

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

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}}

規則を適用

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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