Given primitive `F(x)=1/(x+2) -1/(x+1)` , what is f(x)?

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You need to evaluate the function `f(x)` whose primitive is `F(x)` , hence, you need to use the following relation, such that:

`F'(x) = f(x)`

You need to differentiate the primitive `F(x)` with respect to x, using the quotient rule, such that:

`F'(x) = (1'(x+2) - 1*(x+2)')/((x+2)^2) - (1'(x+1) - 1*(x+1)')/((x+1)^2)`

`F'(x) = -1/((x+2)^2) - 1/((x+1)^2)`

**Hence, evaluating the function `f(x)` , under the given conditions, yields **`f(x) = -1/((x+2)^2) + 1/((x+1)^2).`

`F(x)=(x+2)^(-1)-(x+1)^(-1)`

By deffinition of primitive

`d/(dx) (F(x))=f(x)`

`Thus`

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

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

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