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TS EAMCET202410 May 2024Morning ShiftMathematicsDifferentiationActual

If y= ⁻¹ ( 6 x-2 x^2-4 2 x^2-6 x+5 ) then d y d x =

Options

  1. A2 3 x-x^2-2
  2. B2 3 x-x^2-2
  3. C2 2 x^2-6 x+5
  4. D2 2 x^2-6 x+5

Correct answer

D. 2 2 x^2-6 x+5

Step-by-step solution

y= ⁻¹ ( 6 x-2 x^2-4 2 x^2-6 x+5 ) Let 6 x-2 x^2-4 2 x^2-6 x+5 =v d v d x = 6-4 x (2 x^2-6 x+5 )^2 Now, y= ⁻¹ v d y d x = -1 1-v^2 d v d x aligned & = -1 1- ( 6 x-2 x^2-4 2 x^2-6 x+5 )^2 6-4 x (2 x^2-6 x+5 )^2 & = - (2 x^2-6 x+5 ) (2 x-3)^2 -2(2 x-3) (2 x^2-6 x+5 )^2 = 2 (2 x^2-6 x+5 ) . aligned

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