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MHT CET202525 Apr 2025Morning ShiftMathematicsDifferentiationActual

If y = ₃ ( ₃ x ) then dy d x at x=3 is

Options

  1. A1 3 ( 3)⁻³
  2. B1 3 ( 3)
  3. C1 3 1 ( 3)⁻³
  4. D1 3 ( 3)⁻²

Correct answer

D. 1 3 ( 3)⁻²

Step-by-step solution

Given y = ₃( ₃ x) , the derivative is found using the chain rule and the logarithmic differentiation formula. Let u = ₃ x , so y = ₃ u . Then dy du = 1 u 3 and du dx = 1 x 3 . Applying the chain rule, dy dx = 1 ( ₃ x)( 3) 1 x 3 = 1 x ( ₃ x)( 3)^2 . Evaluating at x = 3 , and noting ₃ 3 = 1 , gives . dy dx |_ x=3 = 1 3 ( 3)^2 , which corresponds to option D .

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