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
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