Find and simplify the different quotient

f(x+h)-f(x) / h

f(x)=2/x

f(x+h)-f(x) / h =???? simplify

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f(x)=2/x， f(x+h)=2/(x+h)

f(x+h)-f(x) / h ={(2/x)-[2/(x+h)]}/h=[2(x+h)-2x]/xh(x+h)=2h/[xh(x+h)]=2/[x(x+h)]

as h goes to 0 you get f(x+h)-f(x) / h =2/x^2

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