AP EAMCET201923 Apr 2019Morning ShiftMathematicsDifferentiationActual
If (x= ) and (y= p ), then ( (1-x^2 ) y₂= )
Options
- A(x y₁-p^2 y )
- B(p^2 y-x y₁ )
- C(x y₁ )
- D(p^2 y )
Correct answer
A. (x y₁-p^2 y )
Step-by-step solution
Given, (x= ) and (y= p ) ( d y d =-p p ) and ( d x d = ) ( d y d x =- p p =-p 1-y^2 1-x^2 ) ( 1-x^2 d y d x =-p 1-y^2 ) ( ( l -x^2 ) ( d y d x )^2=p^2 ( l -y^2 ) ) (On squaring both sides) ( -2 x ( d y d x )^2+ ( l -x^2 ) 2 d y d x ( d^2 y d x^2 )=-p^2 2 y d y d x ) (On differentiating both sides) ( -x d y d x + (1-x^2 ) d^2 y d x^2 =-p^2 y ) ( ( l -x^2 ) y₂=x y₁-p^2 y ) Hence, option (a) is correct.