code: def test_derivative_appellf1():
      from sympy.core.function import diff
  
      a, b1, b2, c, x, y, z = symbols("a b1 b2 c x y z")
      assert (
          diff(appellf1(a, b1, b2, c, x, y), x)
          == a * b1 * appellf1(a + 1, b2, b1 + 1, c + 1, y, x) / c
      )
      assert (
          diff(appellf1(a, b1, b2, c, x, y), y)
          == a * b2 * appellf1(a + 1, b1, b2 + 1, c + 1, x, y) / c
      )
      assert diff(appellf1(a, b1, b2, c, x, y), z) == 0
      assert diff(appellf1(a, b1, b2, c, x, y), a) == Derivative(
          appellf1(a, b1, b2, c, x, y), a
      )
  
imports: from sympy.core.containers import Tuple
  from sympy.core.function import Derivative
  from sympy.core.numbers import I, Rational, oo, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.exponential import exp, log
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import cos
  from sympy.functions.special.gamma_functions import gamma
  from sympy.functions.special.hyper import appellf1, hyper, meijerg
  from sympy.series.order import O
  from sympy.abc import x, z, k
  from sympy.series.limits import limit
  from sympy.testing.pytest import raises, slow
  from sympy.core.random import random_complex_number, verify_numerically, test_derivative_numerically
label_desc: Use image node_id 15 for calling a global function with example usage: test_derivative_appellf1() without return types