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Aby Alex Grade: 12
        

Differentiate tan−1   [ (1+x2)1/2 - (1-x2)1/2 ]  w.r.t x ?  


                              ———————————


                             (1+x2)1/2 + (1-x2)1/2

7 years ago

Answers : (2)

Badiuddin askIITians.ismu Expert
147 Points
										

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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Badiuddin

7 years ago
Aby Alex
33 Points
										

But  our school exams need substitution method


like , x=sin1/2 Θ, cosΘ etc...

7 years ago
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