Derivation of $1 = x^2+y^2$ with respect to time I am studying differential algebraic equations. Given the following equation:
$1 = x^2+y^2$
Differentiate this equation with respect to time.
The correct solution is:
$0=2x \dot x + 2y \dot y $
But why? 
My wrong idea was:
$0=2x+2y$
Thank you very much!

If $x=x(t)$ then
$$
\frac{d}{dt} \left[x^2\right] = 2x \frac{dx}{dt}
$$
and same for $y$ by the Chain Rule.
