AP EAMCET202022 Sep 2020Evening ShiftMathematicsDifferentiationActual
If x^2+y^2 = ⁻¹ ( x y ) , then d y d x is equal to
Options
- Ay-x y+x
- Bx+y x-y
- C1 y+x
- D1 x-y
Correct answer
A. y-x y+x
Step-by-step solution
x^2+y^2 = ⁻¹ ( x y ) Differentiate w.r.t ' x ' on both sides, gathered 1 x^2+y^2 d d x ( x^2+y^2 )= 1 1+ ( x y )^2 d d x ( x y ) 1 x^2+y^2 1 2 x^2+y^2 d d x (x^2+y^2 ) = 1 y^2+x^2 y^2 1 y-x y^ y^2 1 2 (x^2+y^2 ) (2 x+2 y y^ )= y^2 (x^2+y^2 ) y-x y^ y^2 x+y y^ =y^2 ( y-x y^ y^2 ) gathered aligned x+y y^ & =y-x y^ y y^ +x y^ & =y-x y^ (x+y) & =y-x y^ & = y-x x+y d y d x & = y-x y+x aligned Hence, option (1) is correct.