請教一道導數題已知f(x)=(x-2)/[x(x+1)] 求f(x)的導函數

題目：

請教一道導數題
已知f(x)=(x-2)/[x(x+1)] 求f(x)的導函數

解答：

(a/b)' = (a'b - ab')/b^2
f(x)'
= {(x-2)'[x(x+1)] - (x-2)[x(x+1)]'}/[x^2(x+1)^2]
= {x(x+1) - (x-2)(2x+1)}/[x^2(x+1)^2]
= {x^2 + x - 2x^2 + 3x +2}/[x^2(x+1)^2]
= (-x^2 + 4x + 2) /[x^2(x+1)^2]