how to take derivative with respect to two variables?

Question

Imagine we have a function like f(xy), how can one can take derivatives with respect to xy in python? I tried to rename u=x*y and take derivative with respect to u, but it apparently doesn't work.

from sympy import symbols, diff
x, y, z = symbols('x y z', real=True)
f = 4*x*y + x*sin(z) + x**3 + z**8*y
u=x*y
diff(f, x)

and for one step further how can we do that if we don't have the exact definition of f(x*y)? thank you.