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MHT CET20242 May 2024Evening ShiftMathematicsDifferentiationActual

If f (x)= _ x^2 ( _ e x ) , then f ^ (x) at x= e is

Options

  1. A1
  2. B1 e
  3. C1 2 e
  4. D1 4 e

Correct answer

C. 1 2 e

Step-by-step solution

aligned f(x) & = _ x^2 ( _ e x ) & = ( _ e x ) x^2 & = ( _ e x ) 2 x aligned f ^ (x)= 1 2 [ x 1 _ e x ~d ~d x ( x)- ( _ e x ) 1 x ( x)^2 ] f ^ (x)= 1 2 [ 1 x - ( _ e x ) x ( x)^2 ] f ^ ( e )= 1 2 [ 1 e -0 (1)^2 ]= 1 2 e

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