# Uncertainty Derivations/Calculation

**1. The problem statement, all variables and given/known data**

If F = aX

^{n}= f +- f +δf where a is a constant, show f = x

^{n}and [itex]\frac{δf}{f}[/itex] = [itex]\frac{nδx}{x}[/itex].

X = x +- δx

x refers to the average and δx refers to uncertainty in x.

**2. Relevant equations**

The power rule for error propagation shows that the uncertainty is multiplied n times (where n is the power raised).

**3. The attempt at a solution**

I’m having trouble showing that f = x^{n}. Through the use of algebraic manipulation, I was able to get a(x+δx)^{n} = f + δf. I then made the assumption to ignore the constant a and by deduction say x = 5 +- 0.5, set f = x^{n} because it is continuously multiplied by whatever the function x is to the nth power. The second part is easier- mainly I just took the differential δf = n*x^{n-1}δx. This simplifies to [itex]\frac{δf}{f}[/itex] = n[itex]\frac{δx}{x}[/itex]

http://ift.tt/1okxMJI

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