If $y=\frac{1}{2}x\sqrt{a^2-x^2}+\frac{a^2}{2}sin^{-1}\frac{x}{a},$ then $\frac{dy}{dx}=$
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\sqrt{a^2-x^2}$
$\int\sqrt{a^2-x^2}dx=\frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}\sin^{-1}\frac{x}{a}$ [Integration formula]
$\frac{dy}{dx}=\sqrt{a^2-x^2}$