Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20225 Aug 2022Morning ShiftMathematicsDifferentiationActual

If x= - and y= ^n - ^n , then ( d y d x )^2 is equal to

Options

  1. An ^2 ( y ^2-4 ) x ^2
  2. Bn ^2 ( y ^2+4 ) x ^2+4
  3. Cn^2 y^2 x^2 -4
  4. Dn ^2 ( y ^2-4 ) x ^2-4

Correct answer

B. n ^2 ( y ^2+4 ) x ^2+4

Step-by-step solution

aligned & = ( d y d x )^2= ( d y d d x d )^2= d ( ^n - ^n ) d d( - ) d ^2 & = n ^ n -1 - n ^ n -1 (- ) -(- ) ^2 & = n ^ n + n ^ n + ^2 & = n ( ^n + ^n . ( + ) ^2 & = n ^2 ( ^ n + ^ n )^2 ( + )^2 & aligned = n ^2 [ y ^2+4 ] x ^2+4

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