How to make a function that finds the derivative using python? Is there a built-in one?

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- ParthKohli

How to make a function that finds the derivative using python? Is there a built-in one?

- katieb

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- anonymous

Just create a recursive function that multiplies the factor by the exponential and then decrements the exponent with each call.

- anonymous

Binding variables as if you want to find the area of a circle use this
>>>> pi = 3.14159
>>>> radius = 11.2
>>>> area = pi( radius ** 2)
>>>> area = 394.081

- anonymous

Huh? Did I miss something?

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## More answers

- ParthKohli

@chris2332: That doesn't work for other functions... only polynomials.

- anonymous

maybe!!

- anonymous

Something like that?
def derivative(f):
...."""
....Computes the numerical derivative of a function.
...."""
....def df(x, h=0.1e-5):
........return ( f(x+h/2) - f(x-h/2) )/h
....return df

- ParthKohli

Uh... no

- anonymous

Then what derivative do you want?

- anonymous

The mathematical definition of the derivative of a function f(x) at point x is to take a limit as "h" goes to zero of the following expression:
( f(x+h) - f(x) ) / h
An example is given below: the red curve is the function f(x) and the green curve is the tangent line at x (with same slope as the derivative). The blue curve is a line going through x whose slope equals that of the above formula with a non-zero value of h.
A better way of numerically computing the derivative for the same value of "h" is by taking a symmetrical interval around x as follows:
( f(x + h/2) - f(x - h/2) ) / h
This is illustrated in the next picture. As you can see, the two straight lines have much more similar slopes - hence, the value computed for the derivative is going to be more accurate.
The corresponding python code is as follows:
def derivative(f):
...."""
....Computes the numerical derivative of a function.
...."""
....def df(x, h=0.1e-5):
........return ( f(x+h/2) - f(x-h/2) )/h
....return df
And we use it as follows:
# sample function
def g(x): return x*x*x
# first derivative
dg = derivative(g)
# second derivative
d2g = derivative(dg) # == derivative(derivative(g))
# printing the value computed at a given point:
print dg(3)
print dg(3, 0.001)
print dg(3, 1e-10) # smaller h is not always more precise
source : http://aroberge.blogspot.in/2005/04/computing-derivatives-using-python.html

- anonymous

Exactly... that's where I got the snippet from!

- anonymous

@ParthKohli where u r??

- anonymous

from sympy import init_printing, symbols, ln, diff
init_printing()
x,y = symbols('x y')
f = x**2 / y + 2 * x - ln(y)
diff(f,x)
-> 2*x/y +2

- anonymous

I am assuming u do not want to reinvent the wheel, so just use sympy....

- TuringTest

The next Pset in 6.00x has one problem in which to find the derivative of polynomials written as lists. I would show you the program I wrote but I don't want to give out the answer before the due date.

- ParthKohli

Heh, I'm not following that course.

- TuringTest

then I will pm my code to you, but don't give it to anyone taking the course

- ParthKohli

Yup! I discovered this Python group so thought I'd ask...

- anonymous

numPy/sciPy are good too....

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