How Can dv/dx Be Determined to Solve for dv/dt?

[wololo]

Homework Statement

Homework Equations

Chain rule, partial derivation

The Attempt at a Solution

dv/dt=dv/dx*dx/dt+dv/dy*dy/dt
dx/dt=-4t -> evaluate at (1,1) =-4
dv/dt=-4dv/dx+4(-2)
dv/dt=-4dv/dx-8

How can I find the missing dv/dx in order to get a value for dv/dt? Thanks!

 

[mfb]

Did you expand the other derivatives to see if you get additional constraints from them?