Find dy/dx if x^2+y^2=2xy
A. x/(x-y)
B. (y+x)/(y-x)
C. 1
D. -x/y
E. None of these
Do I equal it to 0 and use implicit rule?
To find dy/dx using the given equation x^2 + y^2 = 2xy, we need to take the derivative of both sides of the equation with respect to x using implicit differentiation.
First, differentiate each term with respect to x using the chain rule:
d/dx(x^2) = 2x
d/dx(y^2) = 2y * dy/dx
d/dx(2xy) = 2y + 2x * dy/dx
Applying implicit differentiation, we can rewrite the equation as:
2x + 2y * dy/dx = 2y + 2x * dy/dx
Now, isolate dy/dx to one side:
2y * dy/dx - 2x * dy/dx = 2y - 2x
Factoring out dy/dx:
dy/dx (2y - 2x) = 2y - 2x
Divide both sides by (2y - 2x):
dy/dx = (2y - 2x) / (2y - 2x)
Now, simplify the expression:
dy/dx = 1
Therefore, the correct answer is C. 1.