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Question

Find dydxin the following questions:

y=sin1(1x21+x2),0<x<1.


Solution

Substitute x = tan1x=θ

  y=sin1(1tan2θ1+tan2θ)=sin1(cos 2θ)y=sin1{sin(πx2θ)}

   y=π22θ    y=πx2tant1x

Differentiating both sides w.r.t. x, we get

dydx=ddx(π2)2ddx(tant1x)

dydx=021+x2     dydx=21+x2   (ddxtan1x=11+x2)

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