`P rov et h a t 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 each term separately and then combine the results.

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