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KCET2015MathematicsInverse Trigonometric Functions

If ( y= ( 1-x² 1+x² ) ), then ( d y d x ) is equal to

Options

  1. A( -4 x 1-x⁴ )
  2. B( 4 x³ 1-x⁴ )
  3. C( 1 4-x⁴ )
  4. D( - 4 x³ 1-x⁴ )

Correct answer

A. ( -4 x 1-x⁴ )

Step-by-step solution

[ array l y= ( 1-x² 1+x² ) d y d x = 1 1-x² 1+x² [ d (1-x² ) d x (1+x² )- d (1+x² ) d x (1-x² ) ] array ] (Using quotient rule) [ array l d y d x = 1+x² 1-x² [ -2 x (1+x² )-2 x (1-x² ) (1+x² )² ] d y d x = 1 1-x² [ -2 x (1+x²+1-x² ) (1+x² ) ] d y d x = [ -4 x 1²- (x² )² ] d y d x = [ -4 x 1-x⁴ ] array ]

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