What is the maximum possible relative error in Z,where Z=AⁿB^m.
 

Dear Student,

Please find below the solution to the asked query:

Given that,

$$\begin{gathered} Z=A^n{B}^m \\ Apply \log on both sides, \\ \ln \left(Z\right)=\ln \left(A^n{B}^m\right)\Rightarrow ln\left(Z\right)=ln\left(A^n\right)+ln\left(B^m\right) \\ Differente above equation both sides with Z. \\ \Rightarrow \frac{1}{Z}\frac{dZ}{dZ}=\frac{d}{dZ}\left\{ln\left(A^n\right)+ln\left(B^m\right)\right\}=\frac{d}{dZ}\left\{ln\left(A^n\right)\right\}+\frac{d}{dZ}\left\{ln\left(B^m\right)\right\} \\ \Rightarrow \frac{1}{Z}=n\frac{1}{A}\frac{dA}{dZ}+m\frac{1}{B}\frac{dB}{dZ} \\ \Rightarrow \frac{dZ}{Z}=n\frac{dA}{A}+m\frac{dB}{B} \end{gathered}$$

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