MHT CET202415 May 2024Morning ShiftMathematicsDifferentiationActual
If x=2 - 2 and y=2 - 2 , then d ^2 y ~d x^2 is equal to
Options
- A3 2 3 2
- B3 2 3 2 3 2
- C3 2 ^2 3 2
- D^2 3 2
Correct answer
C. 3 2 ^2 3 2
Step-by-step solution
To solve this problem, we need to find d y d x^2 given the parametric equations: x=2 - 2 , y=2 - 2 . Compute d x d and d y d . Compute d x / d : d x d =-2 +2 2 . Using the identity 2 =2 , we get: d x d =-2 +4 =2 (-1+2 ) Compute d y / d : d y d =2 -2 2 Using the identity 2 =2 ^2 -1 , we get: d y d =2 -4 ^2 +2=2 ( +1-2 ^2 ) . Compute d y d x . d y d x = d y d d x d = 2 ( +1-2 ^2 ) 2 (-1+2 ) = +1-2 ^2 (-1+2 ) . Simplify d y d x . Factor the numerator and denominator where possible. Compute d d ( d y d x ) and then d^2