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Question

Find dydx, if y=sin1(2x1x2), 12<x<12.

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Solution

Putx=sinθθ=sin1x12<x<1212<sinθ<12sin112<θ<sin112π4<θ<π4π2<2θ<π22θ(π2,π2)sin1(sin2θ)=2θsin1(2sinθcosθ)=2θsin1(2×x1x2)=2sin1xy=2sin1xdydx=21x2

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