from jax import jvp, grad

def f(x,y):
  return x + y**2

def freeze(f, argnum, val):
  def _f(arg):
    args = [val, arg] if argnum == 0 else [arg, val]
    return f(*args)
  return _f

def mixed_jvp(f, order, primals, tangents):
  frozen_func = freeze(grad(f, order[0]), argnum=order[1], val=primals[order[0]])
  return jvp(frozen_func, (primals[order[1]],), tangents)

mixed_jvp(f, order=(0,1), primals=(2., 3.), tangents=(1.,))