- #1
JC2000
- 186
- 16
- Homework Statement
- Given ##Z = A/B##. Prove that ##\frac{\delta Z}{Z} = \frac{\delta A}{A} \pm \frac{delta B}{B}##
- Relevant Equations
- ##Z=\frac A b\implies \log(Z)=\log(A)-\log(B)## making
##\frac{\Delta Z}Z=\frac{\Delta A}A+\frac{\Delta B}B##
My Question :
Shouldn't differentiating ##-log B## give ##\frac{-\delta B}{B}##?
(Note : A, B and Z are variables not constants)
By extension for ##Z=A^a \,B^b\, C^c## where ##c## is negative, should ##\frac{\Delta Z}Z=|a|\frac{\Delta A}A+|b|\frac{\Delta B}B-|c|\frac{\Delta C}C##?
Shouldn't differentiating ##-log B## give ##\frac{-\delta B}{B}##?
(Note : A, B and Z are variables not constants)
By extension for ##Z=A^a \,B^b\, C^c## where ##c## is negative, should ##\frac{\Delta Z}Z=|a|\frac{\Delta A}A+|b|\frac{\Delta B}B-|c|\frac{\Delta C}C##?