# Deceptively Simple???

### Deceptively Simple???

OK, I'be been pounding my head against the wall all morning to trying to figure this out.

This is a real world problem.

1. I have an equation such that X divided by Y = Z.
2. Then, X and Y change at the same time.
3. The difference in Z between Original and Revised in this example is 18,800.
4. I'd like to explain or "break down" the 18,800 in terms of X and Y. "I.e, Of the 18,800, ____ was due to change in X and ____ was due to change in Y."
5. I thought I could understand the impact from each variable by changing one at a time and then add their impact but, it's not equal to changing both at once.
6. How can I quantify the "contribution" that X and Y made discreetly to 18,800??????

See attached image for graphical representation of the problem in table form.
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Guest

### Re: Deceptively Simple???

Approximately, $$dz= d(x/y)= d(xy^{-1})= y^{-1}dx- xy^{-2}dy$$ so the "contribution" of the change in x is (1/y)dx where dx is the change in x and the "contribution" of the change in y is -$$xy^{-2}dy$$ where dy is the change in y.
Guest

### Re: Deceptively Simple???

Thanks for this - much appreciated!
five nights at freddy's

angellavail

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