Multivariable Instantaneous rate of change clarification

When you are computing the instantaneous rate of change for f(x,y) what do you take the derivative with respect to?

for example, for

f(x,y)=(sin(πx)cos(πy),yexy,x2+y3)

If I was to find the instantaneous rate of change for all 3 of these functions going through (1,2) with the velocity vector (3,-2) would I just take ddx of all of the functions at (3,-2)?

When you are computing the instantaneous rate of change for f(x,y) what do you take the derivative with respect to?

for example, for

f(x,y)=(sin(πx)cos(πy),yexy,x2+y3)

If I was to find the instantaneous rate of change for all 3 of these functions going through (1,2) with the velocity vector (3,-2) would I just take ddx of all of the functions at (3,-2)?