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Unit 02: Differentiation

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. ===Method 1=== $$ \begin{aligned} \frac{d}{dx}\left(\frac{x+1}{x-1}\right) &= \frac{(x-1)\frac{d}{dx}... (x-1)^{-1} $$ Now $$ \begin{aligned} \frac{d}{dx}\left(\frac{x+1}{x-1}\right) &=\frac{d}{dx}\left(1+2(x-1)^{-1}\right)\\ &= 0-2(x-1)^{-2}(1)\\ &= \frac{-2}{(x