y=x^[x^(1/2)]
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y=x^[x^(1/2)]y=x^[x^(1/2)]y=x^[x^(1/2)]lny=x^0.5lnxy''/y=(x^0.5)''lnx+x^0.5(lnx)''=0.5/x^0.5*lnx+x^0.5/
y=x^[x^(1/2)]
y=x^[x^(1/2)]
y=x^[x^(1/2)]
lny=x^0.5lnx
y'/y=(x^0.5)'lnx+x^0.5(lnx)'
=0.5/x^0.5*lnx+x^0.5/x
=(0.5lnx+1)/x^0.5
所以y'=y*(0.5lnx+1)/x^0.5
=x^(x^0.5) *(0.5lnx+1)/x^0.5
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