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NDA2012MathematicsDifferentiationActual

Consider the following statements : 1. If y= ( x+ x) , then d y d x = x . 2. If y= ( cosec x- x) , then d y d x = cosec x . Which of the above is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

C. Both 1 and 2

Step-by-step solution

aligned & y= _e( x+ x) & d y d x = 1 x+ x d d x ( x+ x) aligned aligned & = 1 x+ x ( x x+ ^2 x ) & = ( x+ x) x ( x+ x) = x aligned y= _ ( cosec x- x) d y d x = 1 cosec x- x d d x ( cosec x- x) aligned & = 1 cosec x- x (- cosec x x+ cosec ^2 x ) & = cosec x( cosec x- x) ( cosec x- x) = cosec x aligned Both 1 and 2 are correct.

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