Question

what is the derivative of lnx^x

Answer 1

ln(x^x) or ln(x)^x?

Answer 2

lnx^x

Answer 3

Uh, so is it ln(x)^x?

Answer 4

what he really wanted to ask is whether its
\(\ln (x^x)\)
or
\((\ln x)^x\)
first or 2nd ?

Answer 5

Yes.

Answer 6

i guess its first, if yes, use the log property that
\(\large \ln a^b=b\ln a\)

Answer 7

then differentiate it using product rule, do you know the product rule ?

Answer 8

Yes it is the first one and I will give it a try with the product rule. I tried applying the power rule but soon into the problem i realized it was a wrong choice i picked. Thanks for the tip.

Answer 9

hmm. welcome :) if you don't get it after u tried or if you want to verify what you got or if you have any doubts, you can ask :)

Answer 10

worked out thanks.

Answer 11

good!

Answer 12

i got lnx +1 as my solution which is correct.

Answer 13

yup, it is correct :)

Answer 14

oh, and by the way,
\(\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\)

Answer 15

Thanks