(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

3. 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~

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

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