Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202418 May 2024Morning ShiftMathematicsDifferentiationActual

If x=3 [ t- ( t 2 ) ] and y=6 [ t+ ( t 2 ) ] then d y d x =

Options

  1. A2 ^2 t 1+ t t
  2. B2 ^2 t 1+ 2 t
  3. C2 ^2 t 1+ t t
  4. D1+ 2 t 1+ 2 t

Correct answer

C. 2 ^2 t 1+ t t

Step-by-step solution

Given, x=3 [ t- ( t 2 ) ] and y=6 [ t+ ( t 2 ) ] Now, d x d t =3 [ t+ cosec ^2 t 2 2 t 2 ]=3 [ t+ 1 t ] d x d t = 3(1+ t t) t and d y d t =6 [- t+ ^2 t 2 2 t 2 ]=6 (- t+ 1 t ) d y d t = 6 ^2 t t Since d y d x = d y d t d x d t = 6 ^2 t t 3(1+ t t) t d y d x = 2 ^2 t 1+ t 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 AP EAMCET PYQs