derivative y=8arcsin(x/4)-(xsqrt(16-x^2))/2

解

導関数

y = 8 arcsin (\frac{x}{4}) - \frac{x 16 - x ^{2}}{2}

\frac{x ^{2}}{- x ^{2} + 16}

解答ステップ

\frac{d}{d x} (8 arcsin (\frac{x}{4}) - \frac{x 16 - x ^{2}}{2})

和/差の法則を適用:

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

= \frac{d}{d x} (8 arcsin (\frac{x}{4})) - \frac{d}{d x} (\frac{x 16 - x ^{2}}{2})

\frac{d}{d x} (8 arcsin (\frac{x}{4})) = \frac{8}{16 - x ^{2}}

\frac{d}{d x} (\frac{x 16 - x ^{2}}{2}) = \frac{8 - x ^{2}}{16 - x ^{2}}

= \frac{8}{16 - x ^{2}} - \frac{8 - x ^{2}}{16 - x ^{2}}

簡素化

\frac{8}{16 - x ^{2}} - \frac{8 - x ^{2}}{16 - x ^{2}} : \frac{x ^{2}}{- x ^{2} + 16}

= \frac{x ^{2}}{- x ^{2} + 16}