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Unit 02: Differentiation

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}$ with respect to $x$. ===Method 1=== $$ \begin{aligned} \frac{d}{dx}\left(\frac{x+1}{x-1}\right) &= \f... ac{x-1-x-1}{(x-1)^2}\\ &= \frac{-2}{(x-1)^2} \end{aligned} $$ ===Method 2=== By converting improper to pr... }= 1+\frac{2}{x-1}=1+2(x-1)^{-1} $$ Now $$ \begin{aligned} \frac{d}{dx}\left(\frac{x+1}{x-1}\right) &=\fr... &= 0-2(x-1)^{-2}(1)\\ &= \frac{-2}{(x-1)^2} \end{aligned} $$ This was a simple example but try it to fi