derivative of sqrt(4-x^2)+2arcsin(x/2)

解

\frac{d}{d x} (4 - x^{2} + 2 arcsin (\frac{x}{2}))

\frac{- x + 2}{- x ^{2} + 4}

解答ステップ

\frac{d}{d x} (4 - x^{2} + 2 arcsin (\frac{x}{2}))

和/差の法則を適用:

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

= \frac{d}{d x} (4 - x^{2}) + \frac{d}{d x} (2 arcsin (\frac{x}{2}))

\frac{d}{d x} (4 - x^{2}) = - \frac{x}{4 - x ^{2}}

\frac{d}{d x} (2 arcsin (\frac{x}{2})) = \frac{2}{4 - x ^{2}}

= - \frac{x}{4 - x ^{2}} + \frac{2}{4 - x ^{2}}

規則を適用

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

= \frac{- x + 2}{- x ^{2} + 4}