How do you evaluate a derivative in python?

Question

I'm a beginner in python. I've recently learned about Sympy and its symbolic manipulation capabilities, in particular, differentiation. I am trying to do the following in the easiest way possible:

1. Define f(x,y) = x^2 + xy^2.
2. Differentiate f with respect to x. So f'(x,y) = 2x + xy^2.
3. Evaluate the derivative, e.g., f'(1,1) = 2 + 1 = 3.

I know how to do 1 and 2. The problem is, when I try to evaluate the derivative in step 3, I get an error that python can't calculate the derivative. Here is a minimal working example:

import sympy as sym
import math


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


x, y = sym.symbols('x y')

def fprime(x,y):
    return sym.diff(f(x,y),x)

print(fprime(x,y)) #This works.

print(fprime(1,1)) 

I expect the last line to print 3. It doesn't print anything, and says "can't calculate the 1st derivative wrt 1".

Solution

Your function fprime is not the derivative. It is a function that returns the derivative (as a Sympy expression). To evaluate it, you can use .subs to plug values into this expression:

>>> fprime(x, y).evalf(subs={x: 1, y: 1})
3.00000000000000

If you want fprime to actually be the derivative, you should assign the derivative expression directly to fprime, rather than wrapping it in a function. Then you can evalf it directly:

>>> fprime = sym.diff(f(x,y),x)
>>> fprime.evalf(subs={x: 1, y: 1})
3.00000000000000

Comments

[Quartal]

@user46944 I haven't used sympy so I'm not sure how it works exactly but if you changed it to something like this def fprime(xValue, y): return sym.diff(f(valueX, y),x) I think it should work

[BrenBarn]

@user46944: No, because fprime is still a sympy expression, and you don't evaluate sympy expressions by calling them. You have to use evalf.

[Quartal]

@user46944 x, y = sym.symbols('x y') this line sets x value right?

[Quartal]

@user46944 In the function def f(x,y): return x2 + x*y2 x takes the value which you call the function with

[BrenBarn]

@user46944: For that you could do fprime.subs(y, 1). I don't think there is a way to make a sympy object that can be manipulated symbolically (e.g., differentiated) but can also be called to substitute values like that. To substitute values you need to to use .subs or .evalf.

[BrenBarn]

@user46944: Sympy expressions and Python functions are two different things. Sympy expressions can be differentiated, but not called. Python functions can be called, but not differentiated. Your original question doesn't say anything about plotting or these other issues you're raising in the comments. If you have some additional question, you should probably ask it as a separate question, including in the text of that question the code you're trying to use.

[BrenBarn]

@user46944: It's not differentiating your function, it's differentiating the return value of your function, which is a sympy expression.