y=x^x+x^x^2 求y'2.lim x→3+ [cosx In(x-3)]/[In(e^x-e^3)] 最重要的是
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1.y1=x^x lny1=xlnx y1'/y1=lnx+x/x=lnx+1 y1'=x^x(lnx+1) y2=x^x^2 lny2=x^2lnx y2'/y2=2xlnx+x^2/x=x(2lnx+1) y2'=x^x^2*x(2lnx+1)=x^(x^2+1)(2lnx+1) y'=y1'+y2'=x^x(lnx+1)+x^(x^2+1)(2lnx+1) 2.lim x→3+ [cosx In(x-3)]/[In(e^x-e^3)] =lim x→3+ (cosx)*limx→3+[In(x-3)/In(e^x-e^3)] =cos3lim x→3+[(e^x-e^3)/e^x(x-3)] =cos3lim x→3+[(1-e^(3-x))/(x-3)] =cos3lim x→3+[(e^(3-x)] =cos3

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