Should I Use Total or Partial Differentiation in Absolute Error Calculation?

  • Context: Undergrad 
  • Thread starter Thread starter Chemist@
  • Start date Start date
  • Tags Tags
    Calculation Error
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
3 replies · 1K views
Chemist@
Messages
115
Reaction score
1
The absolute error of the quantity p should be calculated.
p=a*b where a and b are two variables.
By taking ln on both sides:
lnp=lna+lnb, then differentiating:
dp/p=da/a+db/b
dp=abolute error
Should I have used total or partial differential in the differentiation step?
 

Discussion

Physics news on Phys.org
Doesn't matter. [itex]da[/itex] or [itex]\partial a[/itex] or [itex]\Delta a[/itex], they all represent the error in measuring a.
 
Which is the most correct to use when I differentiate a function of two variables? Partial derivative?
 
Well, now that I think, [itex]d[/itex] is the correct one. Because you're actually differentiating [itex]\ln p[/itex] w.r.t. p regardless of what p depends on! The same for other two logarithms.
Anyway, I've heard several methods for calculating absolute errors. But the one I prefer, is the following:
[itex]E[f(x_1,x_2,...,x_n)]=\sqrt{\sum_{k=1}^n (\frac{\partial f}{\partial x_k} dx_k)^2}[/itex]
Because it obviously gives the maximum change in f for given changes in its arguments.