# Δ(Δx)/Δ(Δy) problem?

Does Δ(Δx)/Δ(Δy) exist in mathematics and physics?

## The Attempt at a Solution

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rock.freak667
Homework Helper
If by Δx and Δy you mean the change in x and change in y, then yes it does exist. For example, if you have a graph of x and t (displacement-time), you can get the velocity at some point by computing Δx/Δt. If you want the acceleration you would compute Δ(Δx)/Δ(Δt).

if you want to calculate the acceleration, you need calculate like (Δ(Δx/Δt)/Δt but not Δ(Δx)/Δ(Δt). Am I right? Thanks a lot.

rock.freak667
Homework Helper
Yeah I left out the extra t. Sorry there.

This means that Δ(Δx)/Δ(Δy) does not exist in mathematics. Are you agreeing? Thanks a lot.

HallsofIvy
Homework Helper
Any calculation can exist in mathematics. I may not give you what you want!
Assuming that by "$\Delta x$", you mean "a slight change in x" then $\Delta(\Delta x)/\Delta(\Delta y)$ certainly does exist. But it is NOT an approximation to the second derivative if that was what you meant.

I mean that Δ(Δx)/Δ(Δy) does have any physics or mathematical meaning. Do you agree? If not, can you tell me what is the meaning of Δ(Δx)/Δ(Δy)? Sure, you can do any calculation as you want.

Sorry. I should say:

I mean that Δ(Δx)/Δ(Δy) does not have any physics or mathematical meaning. Do you agree? If not, can you tell me what is the meaning of Δ(Δx)/Δ(Δy)? Sure, you can do any calculation as you want.

Sorry. I should say:

I mean that Δ(Δx)/Δ(Δy) does not have any physics or mathematical meaning. Do you agree? If not, can you tell me what is the meaning of Δ(Δx)/Δ(Δy)? Sure, you can do any calculation as you want.
Try an example as see what happens. Say x=t3 and y=t4

What do you get for x, Δx, Δ(Δx), y, Δy, Δ(Δy) and finally for the ratio Δ(Δx)/Δ(Δy), when t is 1.0, 1.1 and 1.2?

See the following example. I think that Δ(Δx)/Δ(Δy) does not exist in mathematics because it doesnot have any physical meaning although you can calculate it.

x y x*y x^2 y^2 x-4 y-6 x*y x^2 y^2 x-VarX y-VarY x*y x^2 y^2
1 8 8 1 64 -3 2 -6 9 4 -1 4 -4 1 16
2 13 26 4 169 -2 7 -14 4 49 -2 7 -14 4 49
3 18 54 9 324 -1 12 -12 1 144 -2 -12 24 4 144
4 23 92 16 529 0 17 0 0 289 8 13 104 64 169
5 28 140 25 784 1 22 22 1 484 -5 16 -80 25 256
6 33 198 36 1089 2 27 54 4 729 0 -63 0 0 3969
7 38 266 49 1444 3 32 96 9 1024 3 28 84 9 784
8 43 344 64 1849 4 37 148 16 1369 -12 -7 84 144 49
9 48 432 81 2304 5 42 210 25 1764 -11 28 -308 121 784
10 53 530 100 2809 6 47 282 36 2209 -20 30 -600 400 900
11 58 638 121 3364 7 52 364 49 2704 -29 8 -232 841 64
12 63 756 144 3969 8 57 456 64 3249 -48 -7 336 2304 49

slope 5 5 -0.058368602