find y' if y=x/(x+y)
Do you take the derivative of the y on the left of the = or no?
I really need help
to make it a bit easier, multiply both sides by (x+y) to clear the fraction ...
$\displaystyle y(x+y) = x$
$\displaystyle xy + y^2 = x$
now take the derivative implicitly ...
$\displaystyle xy' + y + 2y \cdot y' = 1$
$\displaystyle xy' + 2y \cdot y' = 1 - y$
$\displaystyle y'(x + 2y) = 1 - y$
$\displaystyle y' = \frac{1-y}{x+2y}$