It is straightforward to compute the partial derivatives of a function at a point with respect to the first argument using the SciPy function scipy.misc.derivative
scipy.misc.derivative
Yes, it is implemented in sympy. Demo:
sympy
>>> from sympy import symbols, diff >>> x, y = symbols('x y', real=True) >>> diff( x**2 + y**3, y) 3*y**2 >>> diff( x**2 + y**3, y).subs({x:3, y:1}) 3