If u= ⁻¹ ( 1+x² -1 x ) and v= ⁻¹ ( 2 x 1-x² 1-2 x² ) , then d u d v at x=0 is

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Correct answer: A. 1 4

Given u= ⁻¹ ( 1+x² -1 x ) Put x= = ⁻¹ ( -1 ) = ⁻¹ ( 1- )= ⁻¹ ( 2 ² 2 2 2 ) u= ⁻¹ x 2 d u d x = 1 2 (1+x² ) We have, v= ⁻¹ ( 2 x 1-x² 1-2 x² ) Put x= v= ⁻¹ ( 2 2 )= ⁻¹ ( 2 2 )= ⁻¹( 2 )=2 v=2 ⁻¹ x d v d x = 2 1+x² . d u d v = d u d x )= 1 2 (1+x² ) (1+x² ) 2 = 1 4

If u= ⁻¹ ( 1+x² -1 x ) and v= ⁻¹ ( 2 x 1-x² 1-2 x² ) , then d u d v at x=0 is

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