Prove that `d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)x/a}=sqrt(a^2-x^2)`

Explanation

To prove that

\[ \frac{d}{dx}\left(\frac{x}{2\sqrt{a^2 - x^2}} + \frac{a^2}{2 \sin^{-1}\left(\frac{x}{a}\right)}\right) = \sqrt{a^2 - x^2} \]

we will differentiate the left-hand side (LHS) step by step.

...