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**Suppose we have a function [tex] V(x,y)=x^2 + axy + y^2[/tex]**

how do we write

[tex] \frac{dV}{dt} [/tex]

how do we write

[tex] \frac{dV}{dt} [/tex]

For instance if [tex] V(x,y)=x^2 + y^2[/tex], then [tex] \frac{dV}{dt} = 2x \frac{dx}{dt} + 2y \frac{dy}{dt} [/tex]

So, is the solution

[tex] \frac{dV}{dt} = 2x \frac{dx}{dt} + ay\frac{dx}{dt} + ax\frac{dy}{dt} + 2y \frac{dy}{dt} [/tex]