Use the chain rule to differentiate y=1/x^2-2x-1

First we will rewrite y so it is written with a power: y=1/x²-2x-1=(x²-2x-1)^-1 Now let u=x²-2x-1 => du/dx = 2x -2 Writing y in terms of u: y=u^-1 => dy/du= -u^-2 = - 1/u² using the chain rule: dy/dx = dy/du x du/dx =-1/u² x (2x-2) substituting back in the value of u: =-(2x-2)/(x²-2x-1)² = dy/dx