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Find the derivative:

Mathematics
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|dw:1349927470125:dw|
I can easily find the derivative of the ln(x+ln(x+ln(x))) but I cant figure out how to find the derivative of the first part.
i think it will be better to take the log of that part with the respect of e base.

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Other answers:

|dw:1349927833215:dw|
|dw:1349927846691:dw|
yeah.
Okay I had an idea about that. But don't you have to do that for the ln(x+ln(x+ln(x))) as well?
Like I thought you had to take the log of both sides for logarithmic differentiation.
yes,or you may solve the two parts one by one
So I thought you had to:|dw:1349927977970:dw|
Do you do that?
Don't*
and even if you take the ln of ln(x+ln(x+ln(x))),there ain't any problem
Yes yes. I knew that. But is that valid? I though you had to Log both sides of the ENTIRE term.
Ohh? Why not?
yes it is.
How is it valid? Sorry for being stubborn.
sorry to interrupt. but ln(A+B)\(\ne\)ln A + ln B so here you have to differentiate 1st term separately , using ln
Ohh I know @hartnn . I didn't seperate it.
|dw:1349928327564:dw|
that is why you can find the derivatives separately
Lol I know. By I mean why can you ln only the (arcsin)^Tan(x)? I though you had to ln EVERYTHING.
"had to" <---no
why?? if you solve them part by part, you are free to take the ln of one part without changing the other
Ohh. Okay. That explains it.
Fair enough haha...
Could I do this instead? |dw:1349928628192:dw|
For the derivative I mean.
NO! what have u done!!
i couldn't get it @Dido525 :(
You make me chukle @hartnn .
how and why will you do that?
Well the derivative of a^x = a^x *ln(a)
ln y = tan x ln(sin^-1 (x)) diff. this. no other way
Okay okay :P .
Then this question isn't so hard.
is it ? what u get as y' ?
Wait.
Doing it now.
I got: |dw:1349929346410:dw|
For the derivative of (sin-1(x))^(tan(x))
seems correct.
Okay :D . Thanks!

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