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Question

Find dydxin the following questions:

y=cos1(1x21+x2),0<x<1.

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Solution

Let tan1x=θi.e.,x=tant θ

y=cos1(1x21+x2)=y=cos1(1tan2θ1+tan2θ) ( 1tan2θ1+tan2θ=cos 2θ)

y=cos1(cos 2θ)=2 tan1x

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

dydx=2ddx(tan1x)=21+x2 (ddxtan1x=11+x2)


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