SOLUTION: Find f'(x), the derivative of f at X, for F(X) = 1/x

Question 1026732: Find f'(x), the derivative of f at X, for F(X) = 1/x
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find f'(x), the derivative of f at X, for F(X) = 1/x
F'(X) = lim/h>0 f(x+H)- f(x)/h
[f(x+h) - f(x)]/h = [1/(x+h) - 1/x] / h
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=[x - (x+h)]/[x(x+h)]/h = [-h]/[x*h(x+h)] = [-1/[x(x+h)]
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Take the limit as h goes to 0 to get: -1/x^2
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Ans:: f'(F(x)) = -1/x^2
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Cheers,
Stan H.
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