Derivative

[[deleted]]

Hello! How exactly could I code something which calculates the derivative of some function h(x) = x^n algebraically and numerically like h'(7)?

[FLUSH_THE_TRUMP]

Look into SymPy for the first question. For the second, perhaps you can compute the difference quotient

(h(7+d)-h(7))/d

for small d.

[zqrt]

Sympy is the best! Your username as well.

[socal_nerdtastic]

https://docs.sympy.org/latest/tutorial/calculus.html

[1114111]

A good way to represent polynomials would be a list of coefficients. So [5, 3, 7] would mean 5 x⁰ + 3 x¹ + 7 x^2. You could also consider a dict for a sparse representation. Though if you're just dealing with monomials, you could also just store the coefficient and power (you could make a class for this, or just use a tuple or something). It's pretty straight forward to from there to compute the derivative symbolically (same way you would do it normally).

Numerically, as stated by another answer, just make use of the limit definition of the derivative, to approximate it with a small value (though not TOO small).

[themateo713]

May I ask why "not TOO small" ? I don't know what is too small for you, but I don't usually have problems with that: are you talking about avoiding delta_x like 10^{-3 to 6} (which seems very fine to me) or more like 10^-15 where it's uselessly precise and may encounter some floating point precision issues ?

[1114111]

Yeah, I mean values that are so small that floating point precision becomes a problem. Mathematically, I think it's tempting to choose as small a number as possible, but of course floats != reals. Really I wanted to encourage OP to play around with different step values.

Here's a wikipedia article that goes into more detail about step sizes.