Partial derivatives to disaggregate change

[jhs]

Dear All,

I am trying to use partial derivatives to disaggregate the change in a multivariable function between two data points into the change of the respective variables, but am not sure how to do it or even if it is possible. Let me illustrate what I am attempting using the example of a cone:

I.e V= pi*r^2*h/3

For data point 1: r=3 and h=3, V= 28.27
For data point 2: r=3.5 and h=2.5, V=32.07

I want to split it out and say volume increased by x amount due to the 0.5 increase in radius, and decreased y amount due to the 0.5 decrease in height, which if summed together provides the net change in volume between data points 1 and 2. I tried using partial derivatives however the equations don't provide a valid gradient over the long intervals.

Is this calculation possible?

Thanks in advance for any assistance!

 

[tkhunny]

"over the long intergals"

Why would you expect it to do that? The concept of the "differential", or the idea of "linearization", both assume small displacement - generally very small.

You could achieve an exact answer by using the entire formulation.