[SOLVED] Create a function, that is the derivative of a function

Create a function, that is the derivative of a function

I have in my code a function, let's say:

def test_func(x):
    return(3*x**2)

I want my code to calculate the derivative der_test_func of test_func, so that der_test_func is a function, too. Means, I should be able to do

>>> print(der_test_func(5))
>>> 30

Or I should be able to put it inside another function so that it gets handled reasonably, e.g.

def func2(x):
    y = 10*der_test_func(x)
    return(y)

>>> print(func2(5))
>>> 300

I found out that sympy does derivations, which looks at first sight great, but it returns expressions, whereas I want somehow to have a function, so that I give input to it and get output. Any suggestions or workarounds on how to create der_test_func? Tnx

Solution

If you pass a SymPy Symbol into your function then it will be converted to a symbolic expression. You can then differentiate that and make a function to call it:

In [11]: def test_func(x):
    ...:     return 3*x**2
    ...: 

In [12]: x = sympy.symbols('x')

In [13]: f = test_func(x)

In [14]: f
Out[14]: 
   2
3⋅x 

In [15]: f.diff(x)
Out[15]: 6⋅x

In [16]: g = sympy.Lambda(x, f.diff(x))

In [17]: g
Out[17]: x ↦ 6⋅x

In [18]: g(5)
Out[18]: 30

This will work for a simple function like the example given but won't work if your function does more complicated things like using if/else or loops etc.