using Calculs
f(x) = sin(x)
f'(1.0) - cos(1.0)
When I run this, I get an error saying it doesn’t accept 64bit integers. How do I change the type of a function to a real number?
you can use:
f(x) = sin(float(x))
1 Like
for what i see, it seems that x' is not a valid syntax for the derivative of a function, can you try using
derivative(b, 1.0) ?
Yes that works, but the documentation says that b’(1) should work too. The difference though, is that b’ is numeric, while differentiate() is symbolic, and I don’t know how to put symbolic outputs into functions. I can use ForwardDiff.jl to get a numeric result in a formula, but I thought this would look better.
if you want something pretty, you can use unicode:
∂(f,x) = ForwardDiff.derivative(f,x)
∂(b,1.0)
2 Likes
I do quite like that. Is there a way to save differentiate, so that I can plug it into a function, either as a function of x, or a function of an integer?
sorry, i didnt understand, can you give an example of what you want?
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no idea what this will do, and I don’t expect it to work.
δ(x)=differentiate(x^2)
f(x)=δ+5x
f(1)
7
a working version
δ(x)=differentiate(x->x^2)
f(x)=δ(x)+5x
f(1)
7
EDIT; wait, it is symbolic?
Ok, that was surprisingly easy
yes. that’s why I didn’t think I could, lol.
ahh, i see, differenciate has as inputs an String an a series of Symbols, and returns an expression. i dont think that you can add two expressions, the system in that way its not composable
I didn’t think so, or that it might be way to complicated, and not at all worth my time for minor aesthetics, when I have a working numeric option. Do you get why f’(x) is described in the source code though?
i dont know. i checked the source code and i couldnt find any way where ' are defined. maybe submit an issue on the repo?. asking to update the readme?
sure I can do that. like I said, it would be a nice feature, but by no means essential.
It looks like the prime notation was removed last year because it overwrote the adjoint operator: https://github.com/JuliaMath/Calculus.jl/issues/143#issue-536837155
But weirdly this still worked for me just now…
julia> using Calculus
julia> f(x) = sin(x)
f (generic function with 1 method)
julia> f'(1) - cos(1)
0.0
2 Likes
That makes a lot of sense actually. having δ(function) as an opperator would be cool, and having δ(number) as a numeric opperator would be really handy and make neat code. I might suggest that on github. I think that can be done with dictonaries. It would also be cool if δ(x) was a generic function, but I don’t know if that’s practitcal.
something like
δ(x^3)
3x^2
δ(1)
3
δ(3)
27
δ(x)=δ(x^3)
generic function with 1 method
δ(3)
27
d(x)=(δ(x)/3)
generic function with 1 method
d(3)
3
Where did the b come from?
the b is a mistake, but otherwise this works good for finding the derivative at a certain value of x. can this be used with Roots.jl to find x at a certain derivative?