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MHT CET20249 May 2024Morning ShiftMathematicsDifferentiationActual

If for x (0, 1 4 ) , the derivative of ⁻¹ ( 6 x x 1-9 x^3 ) is x g(x) , then g(x) equals

Options

  1. A3 x x 1-9 x^3
  2. B3 x 1-9 x^3
  3. C3 1+9 x^3
  4. D9 1+9 x^3

Correct answer

D. 9 1+9 x^3

Step-by-step solution

Let y= ⁻¹ ( 6 x x 1-9 x^3 ) aligned & = ⁻¹ ( 3 x x +3 x x 1-3 x x 3 x x ) & = ⁻¹(3 x x )+ ⁻¹ 3 x x & y=2 ⁻¹(3 x x ) aligned Differentiating w.r.t. x , we get aligned d y ~d x & = 2 1+(3 x x )^2 ~d ~d x (3 x x ) & = 2 1+9 x^3 9 2 x ~d y ~d x & = 9 x 1+9 x^3 aligned Comparing with d y ~d x = x ~g (x) g (x)= 9 1+9 x^3

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