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AP EAMCET20224 Jul 2022Morning ShiftMathematicsDifferentiationActual

If f x = cot - 1 x x - x - x 2 , then f ' 1 equals

Options

  1. A- 1
  2. Blog e 2
  3. C- log e 2
  4. D3

Correct answer

A. - 1

Step-by-step solution

We have, f x = cot - 1 x x - x - x 2 Differentiating both sides w.r.t. x , we get f ' x = - 1 1 + x x - x - x 2 2 · d d x x x - x - x 2 ⇒ f ' x = - 2 4 + x x - x - x 2 · d d x x x - x - x ⇒ f ' x = - 2 x x + x - x 2 · d d x e x log x - e - x log x ⇒ f ' x = - 2 x x + x - x 2 × e x log x · d d x x log x - e - x log x · d d x - x log x ⇒ f ' x = - 2 x x + x - x 2 x x 1 + log x + x - x 1 + log x ⇒ f ' x = - 2 1 + log x x x + x - x Put

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