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Using the definition of derivate find f ` (x)

f (x) = x - (a/x) , where a is a constant

f ` (x) = lim h->0 [(f(x+h)) – (f(x))]/h

= lim h->0 [((x+h) –(a/(x+h)) -(x-(a/x))]/h

= lim h->0 ([((x+h) –(a/(x+h)) -(x-(a/x))]/h) . (x(x+h))/(x(x+h))

= lim h->0 ((x^3)+(h^2x)-(ax)-(x^3)-(x^2h)+(ax)+(ah))/(h(x^2+xh))

= lim h->0 (h(hx-x^2+a))/(h(x^2+xh)) = (-x^2+a)/x^2

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# Homework Help: Help with a derivative

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