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MHT CET202411 May 2024Evening ShiftMathematicsDifferentiationActual

If f (x)= _ x^2 ( x) , then at x= e , f ^ (x) has the value

Options

  1. A1 e ^2
  2. B1 e
  3. Ce ^ 2
  4. D1 2 e

Correct answer

D. 1 2 e

Step-by-step solution

Let y= _ x^2 ( x) x^ 2 y = x Differentiating w.r.t. x , we get aligned & x^ 2 y ( x) 2 d y ~d x = 1 x & ( x)^2 d y ~d x = 1 2 x & At x= e , f ^ (x)= d y ~d x = 1 2 e aligned [ x^ 2 y = x ]

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