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AP EAMCET202018 Sep 2020Morning ShiftMathematicsDifferentiationActual

If (y= 2 x+ ^2 (2 x+ 4 ) ), then ( d y d x ) at (x= 4 ).

Options

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

Correct answer

A. ( 2 2 +1 )

Step-by-step solution

Given, (y= 2 x+ ^2 (2 x+ 4 ) ) So, at (x= 4 ) ( aligned y & = 2 + ^2 ( 2 + 4 ) & = 2 + ^2 4 = 2 + 1 2 aligned ) Now, as (y^2=2 x+ ^2 (2 x+ 4 ) ) On, differentiating w.r.t. (x ), we get ( aligned 2 y d y d x & =2-2 (4 x+ 2 ) & =2-2 4 x d y d x = 1- 4 x y . d y d x |_ x= 4 & = 1-(-1) 2 + 1 2 = 2 2 +1 aligned )

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