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If y=1+ 1 x + 1 x² + 1 x³ + with |x|>1 , then d y d x =

Options

  1. A-y² x²
  2. By² x²
  3. Cx² y²
  4. Dx² y²

Correct answer

A. -y² x²

Step-by-step solution

Given, y= 1 x + 1 x² + 1 x³ + This is an infinite GP with a=1 and r= 1 x S_ = a 1-r y= 1 1- 1 x y= x x-1 Now, d y d x = (x-1)-x (x-1)² = x-1-x (x-1)² = -1 (x-1)² =- 1 ( x² y² ) =- y² x²

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