CODEWITHSUNDEEP
pythonsympy
Jakob Krukow
Jakob Krukow

Reputation: 71

Python can't evaluate derivatives at a point

I use Jupyter Notebook. How come this does not work when I want to evaluate the partial derivative at the point P?

from sympy import *
P = (-3,-2)
def f(x,y):
    return x**3+3*x**2-9*x+y**3-12*y
def f_x(x,y):
    return diff(f(x,y), x)

When I type f(P[0],P[1]), I get the answer 43.

When I type f_x(x,y), I get the derivative of f wrt. x

Then, when I type f_x(P[0],P[1]), I get this error:

ValueError                                Traceback (most recent call last) <ipython-input-2-2afed429d2a2> in <module>
      7     return diff(f(x,y), x)
      8 
----> 9 f_x(P[0],P[1])

<ipython-input-2-2afed429d2a2> in f_x(x, y)
      5     return x**3+3*x**2-9*x+y**3-12*y
      6 def f_x(x,y):
----> 7     return diff(f(x,y), x)
      8 
      9 f_x(P[0],P[1])

~\anaconda3\lib\site-packages\sympy\core\function.py in diff(f,
*symbols, **kwargs)    2503         return f.diff(*symbols, **kwargs)    2504     kwargs.setdefault('evaluate', True)
-> 2505     return _derivative_dispatch(f, *symbols, **kwargs)    2506     2507 

~\anaconda3\lib\site-packages\sympy\core\function.py in
_derivative_dispatch(expr, *variables, **kwargs)    1945         from sympy.tensor.array.array_derivatives import ArrayDerivative    1946    return ArrayDerivative(expr, *variables, **kwargs)
-> 1947     return Derivative(expr, *variables, **kwargs)    1948     1949 

~\anaconda3\lib\site-packages\sympy\core\function.py in __new__(cls, expr, *variables, **kwargs)    1312             if isinstance(v, Integer):    1313                 if i == 0:
-> 1314                     raise ValueError("First variable cannot be a number: %i" % v)    1315                 count = v    1316           prev, prevcount = variable_count[-1]

ValueError: First variable cannot be a number: -3

Upvotes: 1

Views: 406

Answers (1)

JohanC
JohanC

Reputation: 80509

What you are doing:

f_x(P[0], P[1]) becomes

f_x(-3, -2) becomes

diff(f(-3, -2), -3) becomes

diff(43, -3) which gives an error: you can't calculate the derivative of the constant function 43 towards a number (-3).

In sympy, functions are usually just written as expressions containing symbolic variables (symbols). Derivatives are calculated directly on the expression. Note that diff(f, x) can also be written as f.diff(x), which might be easier to read.

from sympy import symbols

x, y = symbols('x y')
P = (-3, -2)
# let f be a function of x and y:
f = x**3 + 3*x**2 - 9*x + y**3 - 12*y
# calculate the derivative of f towards x
f_x = f.diff(x) # so, f_x = 3*x**2 + 6*x - 9
# now, fill in the values into the derivative:
f_x.subs({x: P[0], y: P[1]}) # 0

Upvotes: 2

Related Questions