Question

How do you differentiate `f(x)=x/(x-1)^2+x^2-4/(1-2x)` using the sum rule?

Answer 1

`f'(x)=-(x+1)/(x-1)^3+2x -8/(1-2x)^2`

Explanation:

`f(x)=x/(x-1)^2+x^2-4(1-2x)^-1`

Use Quotients Rule: `f'(x)=(gf'-fg')/g^2` to find the derivative of the first part `x/(x-1)^2`

`f'(x)=((x-1)^2-x(2(x-1)))/(x-1)^4 +2x +4/(1-2x)^2 xx-2`

`f'(x)=((x-1)[x-1-2x])/(x-1)^4 +2x +4/(1-2x)^2 xx-2`

`f'(x)=-(x+1)/(x-1)^3+2x -8/(1-2x)^2`