Use the limit of definition of the derivative to find the derivative of f(x)= x^

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Your question suggests you want to find the derivative using the definition of derivative, which is: lim h->0 f(x+h) - f(x) / h Substitute in the given function: lim h->0 (1/(x+h)^2 - 1/x^2)/h Multiply out the squared term: lim h->0 (1/(x^2 + 2xh + h^2) - 1/x^2) / h Put over a common denominator: lim h->0 ((x^2 - x^2 - 2xh - h^2) / ((x^2 + 2xh + h^2)*x^2)) / h Simplify: lim h->0 ((-2xh -h^2) / ((x^2 + 2xh + h^2)*x^2)) / h lim h->0 (h(-2x -h) / ((x^2 + 2xh + h^2)*x^2)) / h lim h->0 ((-2x -h) / ((x^2 + 2xh + h^2)*x^2)) Since there is no longer a division by zero, take the limit: ((-2x -0) / ((x^2 + 2x*0 + 0^2)*x^2)) (-2x) / ((x^2)*x^2)) (-2x) / (x^4) -2x / (x^4) -2 / x^3

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