Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202611 April 2026Morning ShiftMathematicsDifferentiationActual

If y = f ( 3 + 2x 3 - 2x ) , where f(x) = ( x) and dy dx = ( A B + C x^2 ) ^2 ( ( 3 + 2x 3 - 2x ) ) , then the respective values of A, B and C are ......

Options

  1. A3, 2, -4
  2. B12, -9, 4
  3. C6, 6, -2
  4. D12, 9, -4

Correct answer

D. 12, 9, -4

Step-by-step solution

Given y = f ( 3 + 2x 3 - 2x ) and f(x) = ( x) y = ( ( 3 + 2x 3 - 2x ) ) Differentiating with respect to x using the chain rule: dy dx = ^2 ( ( 3 + 2x 3 - 2x ) ) d dx ( ( 3 + 2x 3 - 2x ) ) dy dx = ^2 ( ( 3 + 2x 3 - 2x ) ) 3 - 2x 3 + 2x d dx ( 3 + 2x 3 - 2x ) dy dx = ^2 ( ( 3 + 2x 3 - 2x ) ) 3 - 2x 3 + 2x ( 2(3 - 2x) - (-2)(3 + 2x) (3 - 2x)^2 ) dy dx = ^2 ( ( 3 + 2x 3 - 2x ) ) 3 - 2x 3 + 2x 12 (3 - 2x)^2 dy dx = 12 (3 + 2x)(3 - 2x) ^2 ( ( 3 + 2x 3 - 2x ) ) dy dx = 12 9 - 4x^2 ^2 ( ( 3 + 2x 3 - 2x ) ) Comparing with t

Practice Differentiation on Quantrex Academy →

More from Differentiation

The domain of the derivative of the function f(x)= x 1+|x| is 2025If x= 2^ cosec ⁻¹ t and y= 2^ ⁻¹ t ,|t| 1 then d y d x = 2025If (a+ 2 b x)(a- 2 b y)=a^2-b^2 where a>b>0 , then at ( 4 , 4 ) , dy dx = 2025If x y - y x =0 , then d y d x = 2025If y = ( _ x x )^ x , then dy dx = 2025If f(x)=x^ Sec ⁻¹ x , then f^ (2)= 2025If y= x^4 3 x-5 (x^2-3 )(2 x-3) , then ( d y d x )_ x=2 = 2025If x^2+y^2+ y=4 , then the value of d^2 y d x^2 at x=-2 is 2025 Full Differentiation list All MHT CET PYQs