Partial Derivative Superscript?

[zidon]

Hey guys, I'm not super familiar with partial derivatives, so I turned to Wolfram Alpha to help me out with my problem, but there's one think I can't figure out :*(

Nothing like a real world problem to hit somebody with the "you need to learn more math" stick, lol.

Here's my function I'd like to get partial derivatives of

f({x,y,z} + 20 * {f({x+1.1,y+2.2,z+3.3}), f({x+4.4, y+5.5, z+6.6}), f({x + 7.7,y+8.8,z+9.9})}))

Here's one of the partial derivatives I got:



This is wonderful, I just can't figure out what the superscripts mean! (the ({1,0,0})/({0,1,0})/({0,0,1}) things)

If I ignore them, I get the same partial derivative on all axes,
If they mean we replace x, y, and z with those values, then I get all 0s for my derivatives

I am a bit bamboozled. Any push in the right direction would be extremely helpful

Thank you my friends

 

[HallsofIvy]

I don't understand. You say "Here's one of the partial derivatives I got". So was it you who wrote that notation? If not how did it get into your derivative?

I have not seen that notation before but from the use I would guess that "\(\displaystyle f^{(1,0,0)}\)" means the partial derivative with respect to x- what I woud have written \(\displaystyle f_x\).

 

[Dr.Peterson]

If you are saying this was the output from Wolfram Alpha, please show the input, or a link to the output.

Also, show us the source of your problem, so we can see the notation used there. How is function f defined? What does the notation of your input even mean? Your notation f({x,y,z}) appears to be treating f as a function of a set.

But in fact I do find the notation "\(\displaystyle f^{(1,0,0)}\)" here: https://en.wikipedia.org/wiki/Partial_derivative#Notation

 

[zidon]

Thanks HallsofIvy and Dr. Peterson. That actually would make sense for that f[(1,0,0)] would mean the partial derivative with respect to x.

Dr. Peterson, the input is
"derivative f({x,y,z} + 20 * {f({x+1.1,y+2.2,z+3.3}), f({x+4.4, y+5.5, z+6.6}), f({x + 7.7,y+8.8,z+9.9})}))"

I'm actually working with Perlin Noise, so I have a point in 3d space p={x,y,z}.
I have access to the partial derivative of the function f(p), where f is some kind of noise (perlin, simplex, voronoi, etc.)

What I'm trying to do is figure out is how to get the partial derivatives when I do "domain warping" or "domain distortion".
So, if I have
p={x,y,z} (my point in 3d space)
a={1.1,2.2,3.3} //These 3 vectors create the distortion. The current numbers are arbitrary, and were to help me understand wolfram's output
b={4.4,5.5,6.6}
c={7.7,8.8,9.9}
str=20 //the strength of the distortion
Then my final function is
f(p + str * {f(p+a), f(p+b), f(p+c)}
I can compute the partial derivative of f(some vector), but I'm trying to figure out what happens to my partial derivatives after the warp.
In other words, what is:
differentiate f(p + str * {f(p+a), f(p+b), f(p+c)}

My confusion lies around the syntax that wolfram spit out like this

HallsofIvy says that perhaps the above sample means the partial derivative with respect to y of f(str * f(p + a));

You're correct, there is something very simliar on that wikipedia page

This does seem to support HallsofIvy's suggestion,

but any further insight is more than welcome.

I really appreciate both of your help.
Thanks a ton!

PS: sorry for mistakes in notation. I'm new to the site and it's been a while since I encountered any calculus XD