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MHT CET202619 April 2026Morning ShiftMathematicsDifferentiationActual

If y = ⁻¹ ( 1 + 5x 5x ) , then the value of dy dx is

Options

  1. A-5
  2. B5
  3. C- 2 5
  4. D- 5 2

Correct answer

D. - 5 2

Step-by-step solution

Given y = ⁻¹ ( 1 + 5x 5x ) We can simplify the expression inside the inverse trigonometric function using half-angle formulas: 1 + 5x 5x = ( 5x 2 + 5x 2 )^2 ^2 5x 2 - ^2 5x 2 1 + 5x 5x = 5x 2 + 5x 2 5x 2 - 5x 2 Dividing the numerator and the denominator by 5x 2 : 1 + 5x 5x = 1 + 5x 2 1 - 5x 2 = ( 4 + 5x 2 ) Using the complementary angle identity = ( 2 - ) : ( 4 + 5x 2 ) = ( 2 - ( 4 + 5x 2 ) ) = ( 4 - 5x 2 ) Substituting this back into the original equation: y = ⁻¹ [ ( 4 - 5x 2 ) ] y = 4 - 5x 2 Differentiating with

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