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start by setting y=lnx^lnx

take ln of both sides

lny=lnx(ln(lnx))

differentiate

dy/dx(1/y)=(1+ln(lnx))/x

dy/dx=y(1+ln(lnx))/x

we know that y=lnx^lnx so we can just substatute back in

dy/dx=(lnx^lnx)*(1+ln(lnx))/x

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