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AP EAMCET202021 Sep 2020Evening ShiftMathematicsDifferentiationActual

If (y= 1+ x 1- x ), then ( d y d x = )

Options

  1. A( 1 2 ( 1- x 1+ x ) ^2 ( 4 +x ) )
  2. B( 1 2 ( 1- x 1+ x ) ( 4 +x ) )
  3. C( ( 1- x 1+ x ) ^2 ( 4 +x ) )
  4. D( 1 2 ( 1+ x 1- x ) ^2 ( 4 +x ) )

Correct answer

A. ( 1 2 ( 1- x 1+ x ) ^2 ( 4 +x ) )

Step-by-step solution

Given, (y= 1+ x 1- x ) ( aligned d y d x = & 1 2 1- x 1+ x (1- x) ^2 x+(1+ x) ^2 x (1- x)^2 = & 1 2 1- x 1+ x 2 ^2 x (1- x)^2 = & 1 2 1- x 1+ x 2 ( x- x)^2 = & 1 2 1- x 1+ x 1 ( (x+ 4 ) )^2 = & 1 2 1- x 1+ x ^2 ( 4 +x ) aligned ) Hence, option (a) is correct.

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