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Question

If y=x sin-1 x+1-x2, prove that dydx=sin-1 x

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Solution

We have, y=x sin-1x+1-x2
Differentiate it with respect to x,
dydx=ddxx sin-1x+1-x2 =ddxx sin-1x+ddx1-x2 =x ddxsin-1x+sin-1xddxx+121-x2ddx1-x2 =x1-x2+sin-1x-2x21-x2 =x1-x2+sin-1x-x1-x2 =sin-1x

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