Derivative of an exponential function using logarithms (lon-capa)

[Nana-chan]

Homework Statement

What is the derivative of y=x^(13/x^2) with respect to x?

The Attempt at a Solution

I went through multiple techniques to solve this, but all of them have failed so far ._.

In my latest attempt, I took the natural log of both sides:

lny= lnx^(13/x^2)

I then brought the exponent out of the natural log:

lny = 13/x^2*lnx = 13/x^2 * 1/x = 13/x^3

And solved for both natural logs:

1/y*dy/dx = 13/x^3

dy/dx = x^(13/x^2)*(13/x^3)

Lon-capa says this is wrong. It also says that the other method I used is wrong:

d/dx = a^x*ln(a)

x^(13/x^2)*ln(x)*(-26/x^3)

Please help me~

 

[Nana-chan]

This problem is due in 25 mins so I'm shamelessly bumping it up ._.