Question

Find the derivative of
|x|/(x-1)

Answer 1

`\bf \cfracx{x-1}\iff \cfrac{√(x^2)}{x-1}\iff \cfrac{(x^2)^{(1)/(2)}}{x-1} \\\\\\ \textit{using the quotient rule} \\\\\\ \cfrac{dy}{dx}=\cfrac{(1)/(2)(x^2)^{-(1)/(2)}\cdot 2x(x-1)-(x^2)^{(1)/(2)}\cdot 1}{(x-1)^2}`


`\bf \cfrac{dy}{dx}=\cfrac{\frac{x(x-1)-(x^2)^{(1)/(2)}}{(x^2)^{(1)/(2)}}}{(x-1)^2}\implies \cfrac{dy}{dx}=\cfrac{x(x-1)-(x^2)^{(1)/(2)}}{(x^2)^{(1)/(2)}(x-1)^2} \\\\\\\cfrac{dy}{dx}=\cfracx`