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Differentiate tan−1 [ (1+x2)1/2 - (1-x2)1/2 ] w.r.t x ?
———————————
(1+x2)1/2 + (1-x2)1/2
Dear aby
[(1+x2)1/2 - (1-x2)1/2]/[(1+x2)1/2 + (1-x2)1/2]
simplify it
multiply conjugate of denominator both in nominator and denomenator
it will become
[1-(1-x4)1/2]/x2
so now problem become tan-1[1-(1-x4)1/2]/x2
differentiate as normal
answer will come x/(1-x4)1/2
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All the best. Regards,Askiitians ExpertsBadiuddin
But our school exams need substitution method
like , x=sin1/2 Θ, cosΘ etc...
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