 Problem 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}Bc\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}Bc\frac{\Delta C}C##?