Writing Uncertainty in terms of dA, dB, dC

[ZedCar]

Homework Statement

Write down formulae for dX in terms of dA, dB, dC if:

X = [(A) (B^2)] / C

Homework Equations

I'm using the formula below as this corresponds to this relationship.

(dX/X)^2 = (dA/A)^2 + (dB/B)^2

The Attempt at a Solution

For the first line, not the actual solution, I'm getting either:

(dX/X)^2 = (dA/A)^2 + (2dB/B)^2 + (dC/C)^2

or

(dX/X)^2 = (dA/A)^2 + (dB/B)^2 + (dB/B)^2 + (dC/C)^2

Then if I follow through on either line, I get a different answer.

I was wondering which is the correct line to begin with?

I think it's the second option.

Thank you.

 

[tiny-tim]

Hi ZedCar!

(try using the X² button just above the Reply box )

Write down formulae for dX in terms of dA, dB, dC if:

X = [(A) (B^2)] / C

Homework Equations

I'm using the formula below as this corresponds to this relationship.

(dX/X)^2 = (dA/A)^2 + (dB/B)^2

No, you should never get any squares of differentials.

Start again, with lnX = lnA + … ​