# Math Help - derivative of x raise to log

1. ## derivative of x raise to log

find dy/dx of

and answer must be in terms of natural logs

ok i tried taking the natural log of both sides and i got
dy/dx= x^log7(x)[ln(x)/xln(7)+log7(x)/x] but I don't know how to get everything in terms of natural log instead of log7(x)

2. If $y= log_7(x)$, then $x= 7^y= e^{ln(7^y)}= e^{yln(7)}$. From that $ln(x)= yln(7)$ so
$y= log_7(x)= \frac{ln(x)}{ln(7)}$.

3. i keep getting this but its telling me that it isn't the right answer

4. I don't know what you did, but remember that ln(7) is a constant.

How would you differentiate aln(x) ?