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

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Grade 12Differential Calculus

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

———————————

(1+x²)^1/2+ (1-x²)^1/2

Aby Alex

16 Years agoGrade 12

2 Answers

Badiuddin askIITians.ismu Expert

16 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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