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99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

If y= ( ⁻¹ 2 x )^2+ ( ⁻¹ 2 x )^2 , then (1-4 x^2 ) y₂-4 x y₁=

Options

  1. A0
  2. B4
  3. C16
  4. D12

Correct answer

C. 16

Step-by-step solution

We have, y= ( ⁻¹ 2 x )^2+ ( ⁻¹ 2 x )^2 On differentiating both sides w.r.t. x , we get d y d x =2 ⁻¹ 2 x 1 1-(2 x)^2 2+2 ⁻¹ 2 x ( -1 1-(2 x)^2 ) 2 1-4 x^2 d y d x =4 ( ⁻¹ 2 x- ⁻¹ 2 x ) Again differentiating both sides w.r.t. x , we get aligned & 1-4 x^2 y₂+ 1 2 1-4 x^2 (-8 x) y₁ & =4 ( 1 1-4 x^2 2+ 1 1-4 x^2 2 ) & = 1-4 x^2 y₂- 4 x 1-4 x^2 y₁=8 2 1-4 x^2 & (1-4 x^2 ) y₂-4 x y₁=16 aligned

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