If y=u +2e^u and u=1+lynx

y = u + 2e^u 
dy/du = 1 + 2e^u 

u = 1 + ln x 
du/dx = 1/x 

Then dy/dx = dy/du * du/dx 

dy/dx = (1+2e^u) * 1/x 

Now replace u with 1 + ln x 

dy/dx = (1 + 2e^(1+lnx)) * 1/x 
dy/dx = (1 + 2e^1 * e^ln x) * 1/x 
dy/dx = (1 + 2e x) * 1/x 
dy/dx = 1/x + 2e 

Now let x = 1/e. Then 

dy/dx = 1/(1/e) + 2e = e + 2e = 3e