Question

The variable y depends on x according to the equation: x+y=x^2+y^2. Then

a) dy/dx=2x+2y
b) dy/dx = x+y-x^2-y^2
c) dy/dx = 1-2y/1-2x
d) dy/dx = 1-2x/2y-1

Answer 1

implicit differentiation
\[ 1 +y^{\prime}=2x+2yy^{\prime}\]


\[ 1-2x =+2yy^{\prime}-y^{\prime}\]


\[ 1-2x =+(2y-1)y^{\prime}\]

\[ \frac{1-2x}{(2y-1)} =y^{\prime}\]

Answer 2

so D

Answer 3

x+y=x^2+y^2
y=x^2+y^2 -x
dy/dx=2x+2y dy/dx -1
dy/dx-2y dy/dx=2x -1
(1-2y) dy/dx=2x -1
dy/dx=(2x -1)/(1-2y) ................. D)