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AP EAMCET201726 Apr 2017Morning ShiftMathematicsDifferentiationActual

For x^2-4 0 , the value of d d x [ e^x ( x-2 x+2 )^ 3 4 ] at x=3 is

Options

  1. A8 5
  2. B2
  3. C1
  4. D8 e^3 5

Correct answer

A. 8 5

Step-by-step solution

Let y= e^x ( x-2 x+2 )^ 3 4 aligned & = e^x+ ( x-2 x+2 )^ 3 4 =x e+ 3 4 ( x-2 x+2 ) & =x+ 3 4 ( x-2 x+2 ) aligned Now, differentiating w.r.t. x , we get aligned & d y d x =1+ 3 4 d d x ( x-2 x+2 ) & =1+ 3 4 [ x+2 x-2 (x+2) 1-(x-2) 1 (x+2)^2 ] & =1+ 3 4 4 x^2-4 =1+ 3 x^2-4 & At x=3, & ( d y d x )_ x=3 =1+ 3 5 = 8 5 aligned

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