Determine the f′(x) of the function f(x)=11−x f(x+h)−f(x)h=[11−(x+h)]−[11−x]h=11−x−h−11−xh=1−x−(1−x−h)(1−x)(1−x−h)h=1−x−1+x+hh(1−x)(1−x−h)=hh[1−x−h−x+x2+xh]=11−2x−h+x2+xh Thus, f′(x)=limh→0f(x+h)−f(x)h=11−2x−0+x2+x(0)=11−2x+x2
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