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

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


                              ———————————


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

Grade:12

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

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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Aby Alex
33 Points
12 years ago

But  our school exams need substitution method

like , x=sin1/2 Θ, cosΘ etc...

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