Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202521 Apr 2025Morning ShiftMathematicsDifferentiationActual

If ( a + b x) e ^ y x =x , then x^3 ~d ^2 y d x^2 is equal to

Options

  1. A( y dy d x -x )^2
  2. B(x dy d x - y )^2
  3. C(x dy d x + y )^2
  4. D( y dy d x +x )^2

Correct answer

B. (x dy d x - y )^2

Step-by-step solution

Given the equation (a+bx)e^ y x = x , taking the natural logarithm yields y x = x - (a+bx) . Solving for y gives y = x x - x (a+bx) . Differentiating both sides, dy dx = x + 1 - (a+bx) - bx a+bx . Rewriting using the earlier logarithmic relationship, dy dx = y x + 1 - bx a+bx . Simplifying the constant terms produces dy dx = y x + a a+bx . Multiplying through by x gives x dy dx - y = ax a+bx . Differentiating again, d^2y dx^2 = x dy dx -y x^2 - ab (a+bx)^2 . Substituting the previous result yields d^2y dx^2 = a x(a

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