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AP EAMCET202418 May 2024Morning ShiftMathematicsDifferentiationActual

If y= ⁻¹ ( 2-3 x 3-2 x ) then d y d x =

Options

  1. A(3-2 x)^2 13 ^2 x-24 x+13
  2. B-5 x 13 ^2 x-24 x+13
  3. C5 x 13 ^2 x-24 x+13
  4. D-5 x 13 ^2 x-24 x+13

Correct answer

B. -5 x 13 ^2 x-24 x+13

Step-by-step solution

Given, y= ⁻¹ ( 2-3 x 3-2 x ) Now, d y d x = d d x ( ⁻¹ ( 2-3 x 3-2 x ) )= 1 ( 2-3 x 3-2 x )^2+1 d d x ( 2-3 x 3-2 x )= (3-2 x)^2 4+9 ^2 x-12 x+9+4 ^2 x-12 x (3-2 x)(-3 x)-(2-3 x)(-2 x) (3-2 x)^2 = -9 x+4 x 13 ^2 x-24 x+13 d y d x = -5 x 13 ^2 x-24 x+13

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