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NDA2015MathematicsDifferentiationActual

Given that d d x ( 1+x^2+x^4 1+x+x^2 )=A x+B What is the value of A?

Options

  1. A–1
  2. B1
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

Given d d x ( 1+x^2+x^4 1+ x + x ^2 )= d dx [ 1+ x + x ^2+ x ^4- x 1+ x + x ^2 ] aligned & = d d x [1+ x^4-x x^2+x+1 ] & = d d x [1+ x (x^3-1 ) x^2+x+1 ] & = d d x [1+x(x-1)] & = d d x [1+x^2-x ]=2 x-1...(i) aligned Now comparing equation (i) with AX + B , we get A =2 and B =-1 .

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