Resposta:

[tex]f"(x)=\frac{2.lnx-3}{x^3}[/tex]

Explicação passo a passo:

[tex]f(x)=\frac{lnx}{x} \\\\f'(x)=\frac{x*\frac{1}{x} -lnx*1}{x^2}\\\\f'(x)=\frac{1-lnx}{x^2} \\\\f"(x)=\frac{x^2(0-\frac{1}{x})-(1-lnx)*2x }{x^4} \\\\f"(x)=\frac{-x-2x+2xlnx}{x^4} \\\\f"(x)=\frac{2xlnx-3x}{x^4} \\\\f"(x)=\frac{2.lnx-3}{x^3}[/tex]