Question

Find the derivative of
2x - 1/(x - 1)^2

Answer 1

`(dy)/(dx) = 2 + \frac{2}{{(x - 1)}^( 3) }`

Explanation:

`let \: y = 2x - (1)/((x - 1)^(2) ) \\ \\ \implies \: y = 2x - {(x - 1)}^( - 2) \\ \\ differentiating \: w.r.t. \: x \: on \: both \: sides \\ \\ (dy)/(dx) = (d)/(dx) (2x) - (d)/(dx) {(x - 1)}^( - 2) \\ \\ (dy)/(dx) = 2(d)/(dx) (x) - (d)/(dx) {(x - 1)}^( - 2) \\ \\ (dy)/(dx) = 2(1) - ( - 2) {(x - 1)}^( - 2 - 1) (d)/(dx) (x - 1)\\ \\ (dy)/(dx) = 2 + 2 {(x - 1)}^( - 3) (1 - 0)\\ \\ (dy)/(dx) = 2 + 2 {(x - 1)}^( - 3) (1)\\ \\ (dy)/(dx) = 2 + \frac{2}{{(x - 1)}^( 3) }`