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(1/(x+(delta x))-(1/x))/(delta x) find the limit if it exist.?

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(1/(x+(delta x))-(1/x))/(delta x) find the limit if it exist.?

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  1. [1/(x + ∆x) - 1/x] / ∆x =

    [(x- (x + ∆x)) / x(x + ∆x) ] / ∆x =

    [- ∆x / x(x + ∆x) ] / ∆x =

    - 1 / x(x + ∆x) → - 1/x^2 as ∆x → 0

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