Question

Find the derivative of y= (lnx)^x

Answer 1

using logarithmic diffrentiation

Answer 2

Take the ln of both sides. You will get:
lny = ln(xlnx) = lnx + ln(ln(x)); Differentiate and you will get
y' = y*(1+ln(x))/(x ln(x))
Substitute y = (lnx^x) back and simplify

Answer 3

I got an x in my equation. Can you figure out my mistake?

Answer 4

i used the product rule

Answer 5

Ah, I made a slight mistake on my equation. I thought it was ln(x^x). But still, multiply by y both sides and simplify. Remember that y = (ln(x))^x and you should be fine :-)

Answer 6

is my answer right then?

Answer 7

I think yes. Redoing my work, I got: log^x(x) (1/(log(x))+log(log(x)))

Answer 8

After substituing back y.

Answer 9

substituting*

Answer 10

what is log^x(x) in terms of ln?

Answer 11

It's just ln, I wrote it as log rather than ln

Answer 12

Sorry for being confusing, mate.

Answer 13

Ohh i see its okaythanks alot !