Question

x^2(y) = y^2 + 2x

What is dy/dx

and

the coordinates of the stationary points

Answer 1

just remember the product rule and the chain rule

x^2y = y^2 + 2x
2xy + x^2yy' = 2yy' + 2
y'(x^2y-2y) = 2-2xy
y' =

2(1-xy)
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y(x^2-2)