Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2020MathematicsDifferentiation

If x^ x =y^ y , then d y d x is

Options

  1. A- x y
  2. B- y x
  3. C1+ x 1+ y
  4. D1+ ( x y )

Correct answer

C. 1+ x 1+ y

Step-by-step solution

We have, x^ x =y^ y x x=y y 1 x+ x x =y^ y+ y y y^ x+1=y^ ( y+1) d y d x = 1+ x 1+ y

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 COMEDK PYQs