Originally Posted by

**dokrbb** So, I've got such a function: y = x^(log base5 (x)), which I have to differentiate in terms of ln;

I started by solving the equation **y = x^(lnx/ln5) = x^(lnx - ln5) (wonder if here is my mistake)**

Yea this is your mistake. you would only be able to do this if it was $\displaystyle \displaystyle{ x^{\ln \frac{x}{5}} = x^{\ln x - \ln 5}}$

after that ln y = ln x^(lnx - ln5)=> 1/y*y' = (lnx - ln5)'(ln x) + (ln x)'(lnx - ln5) => (1/x - 1/5)(ln x) + (1/x)(lnx - ln5) =>

y' = x^(lnx - ln5)[(1/x - 1/5)(ln x) + ((lnx - ln5)/x)], that's what I got, but putting it in webwork it consideres it as incorrect,

tell me please were is my mistake,

Thanks,