请教一道导数题已知f(x)=(x-2)/[x(x+1)] 求f(x)的导函数？
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(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],5,
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],5,
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