Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
Below is the solution:
x = e^t
y = te^-t
dy/dx = y'/x'
= (1-t)e^-t/e^t
= (1-t)e^-2t
d^2/dx^2 = (x'y"-x"y')/x'^3
= ((e^t)(t-2)e^-t - (e^t)(1-t)e^-t)/e^3t
= (2t-3)e^-3t
or, do it directly
x = e^t, so
y = lnx/x
y' = (1-lnx)/x^2 = (1-t)e^-2t
y" = (2lnx-3)/x^3 = (2t-3)e^-3t
