I am new to calculus, and thought I had my head round the product, quotient and chain rules, but I can't work out how to tackle this:
$ \frac 1{x(x+1)^2} $
Apparently, the first step of the solution is
$ f'(x) = - \frac {(x+1)^2 + 2x(x+1)} { x^2(x+1)^4} $
but I can't work out how this was arrived at. The denominator of the derivative is the square of the denominator of the function, which suggest use of the quotient rule, but by what steps was the numerator of the derivative arrived at? I expect it is my poor algebra and manipulation techniques letting me down. If anyone can recommend a good tool for improving these (as well as answering my question!) I"d be grateful.