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Just create a recursive function that multiplies the factor by the exponential and then decrements the exponent with each call.
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
Huh? Did I miss something?
@chris2332: That doesn't work for other functions... only polynomials.
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
Then what derivative do you want?
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
Exactly... that's where I got the snippet from!
@ParthKohli where u r??
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
I am assuming u do not want to reinvent the wheel, so just use sympy....
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.
Heh, I'm not following that course.
then I will pm my code to you, but don't give it to anyone taking the course
Yup! I discovered this Python group so thought I'd ask...
numPy/sciPy are good too....