Find-the-first-derivative-of-y-x-16-x-2-16sin-1-x-4-

Question Number 152918 by ZiYangLee last updated on 03/Sep/21

Find the first derivative of

y = x \sqrt{16 - x^{2}} + {16 \sin}^{- 1} \frac{x}{4}

Answered by puissant last updated on 03/Sep/21

y = x \sqrt{16 - x^{2}} + 16 a r c s i n (\frac{x}{4})

\frac{d y}{d x} = \sqrt{16 - x^{2}} - \frac{2 x^{2}}{2 \sqrt{16 - x^{2}}} + 16 \frac{\frac{1}{4}}{\sqrt{1 - \frac{x^{2}}{16}}}

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

= \sqrt{16 - x^{2}} + \sqrt{16 - x^{2}} (\frac{16 - x^{2}}{16 - x^{2}})

= 2 \sqrt{16 - x^{2}} . .

Commented by ZiYangLee last updated on 04/Sep/21

thanks sir