Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2009MathematicsDifferentiation

x= 1- y 1+ y d y d x is equal to

Options

  1. A4 (x+1)^2
  2. B4(x-1) (1+x)^3
  3. Cx-1 (1+x)^3
  4. D4 (x+1)^3

Correct answer

B. 4(x-1) (1+x)^3

Step-by-step solution

Given, x 1 = 1- y 1+ y Applying componendo and dividendo, we get array rlrl & & 1+x 1-x = (1+ y )+(1- y ) (1+ y )-(1- y ) & 1+x 1-x = 2 2 y & & y= ( 1-x 1+x )^2 array On differentiating w.r.t. x , we get aligned d y d x & = -2(1+x)^2(1-x)-(1-x)^2 2(1+x) (1+x)^4 & = (1-x)(1+x)(-2-2 x-2+2 x) (1+x)^4 & = 4(x-1) (x+1)^3 aligned

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