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Question

Find dydx of y=sec1(12x21),0<x<12

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Solution

y=sec1(12x21)=cos1(2x21)
Put x=cosθθ=cos1x,
Then we have,
y=cos1(2cos2θ1)=cos1(cos2θ)=2θ=2cos1x
dydx=211x2=21x2

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