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Question

If y=sin1x, show that (1x2)d2ydx2xdydx=0

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Solution

y=sin1x
Differentiating w.r.t to x, we get
dydx=11x21x2dydx=1
Again differentiating w.r.t to x, we get
1x2d2ydx2+dydx.1×(2x)21x2=0
(1x2)d2ydx2xdydx=0

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