Answer:
[tex]\frac{dy}{dx} = 2 + \frac{2}{{(x - 1)}^{ 3} } [/tex]
Step-by-step explanation:
[tex]let \: y = 2x - \frac{1}{(x - 1)^{2} } \\ \\ \implies \: y = 2x - {(x - 1)}^{ - 2} \\ \\ differentiating \: w.r.t. \: x \: on \: both \: sides \\ \\ \frac{dy}{dx} = \frac{d}{dx} (2x) - \frac{d}{dx} {(x - 1)}^{ - 2} \\ \\ \frac{dy}{dx} = 2\frac{d}{dx} (x) - \frac{d}{dx} {(x - 1)}^{ - 2} \\ \\ \frac{dy}{dx} = 2(1) - ( - 2) {(x - 1)}^{ - 2 - 1} \frac{d}{dx} (x - 1)\\ \\ \frac{dy}{dx} = 2 + 2 {(x - 1)}^{ - 3} (1 - 0)\\ \\ \frac{dy}{dx} = 2 + 2 {(x - 1)}^{ - 3} (1)\\ \\ \frac{dy}{dx} = 2 + \frac{2}{{(x - 1)}^{ 3} } [/tex]
