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

Explanation

`frac{d}{d x}{frac{x}{2} sqrt{a^{2}-x^{2}}+frac{a^{2}}{2} sin ^{-1} frac{x}{a}}=sqrt{a^{2}-x^{2}}`

`mathrm{HS}=frac{d}{d x}{frac{x}{2} sqrt{a^{2}-x^{2}}+frac{a^{2}}{2} sin ^{-1} frac{x}{a}}`

`=frac{d}{d x}(frac{x}{2} sqrt{a^{2}-x^{2}})+frac{d}{d x}(frac{a^{2}}{2} sin ^{-1} frac{x}{a})`


=frac{2(a^{2}-x^{2})}{2 sqrt{a^{2}-x^{2}}}

=frac{(a^{2}-x^{2})}{sqrt{a^{2}-x^{2}}}

=sqrt{a^{2}-x^{2}}=R H S

Hence proved
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