## Dido525 3 years ago Find the derivative:

1. Dido525

|dw:1349927470125:dw|

2. Dido525

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.

3. sritama

i think it will be better to take the log of that part with the respect of e base.

4. Dido525

|dw:1349927833215:dw|

5. sritama

|dw:1349927846691:dw|

6. sritama

yeah.

7. Dido525

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?

8. Dido525

Like I thought you had to take the log of both sides for logarithmic differentiation.

9. sritama

yes,or you may solve the two parts one by one

10. Dido525

So I thought you had to:|dw:1349927977970:dw|

11. Dido525

Do you do that?

12. Dido525

Don't*

13. sritama

and even if you take the ln of ln(x+ln(x+ln(x))),there ain't any problem

14. Dido525

Yes yes. I knew that. But is that valid? I though you had to Log both sides of the ENTIRE term.

15. Dido525

Ohh? Why not?

16. sritama

yes it is.

17. Dido525

How is it valid? Sorry for being stubborn.

18. hartnn

sorry to interrupt. but ln(A+B)\(\ne\)ln A + ln B so here you have to differentiate 1st term separately , using ln

19. Dido525

Ohh I know @hartnn . I didn't seperate it.

20. sritama

|dw:1349928327564:dw|

21. sritama

that is why you can find the derivatives separately

22. Dido525

Lol I know. By I mean why can you ln only the (arcsin)^Tan(x)? I though you had to ln EVERYTHING.

23. hartnn

24. sritama

why?? if you solve them part by part, you are free to take the ln of one part without changing the other

25. Dido525

Ohh. Okay. That explains it.

26. Dido525

Fair enough haha...

27. Dido525

Could I do this instead? |dw:1349928628192:dw|

28. Dido525

For the derivative I mean.

29. Dido525

@sritama ,@hartnn

30. Dido525

@hartnn

31. hartnn

NO! what have u done!!

32. sritama

i couldn't get it @Dido525 :(

33. Dido525

You make me chukle @hartnn .

34. sritama

how and why will you do that?

35. Dido525

Well the derivative of a^x = a^x *ln(a)

36. hartnn

ln y = tan x ln(sin^-1 (x)) diff. this. no other way

37. Dido525

Okay okay :P .

38. Dido525

Then this question isn't so hard.

39. hartnn

is it ? what u get as y' ?

40. Dido525

Wait.

41. Dido525

Doing it now.

42. Dido525

I got: |dw:1349929346410:dw|

43. Dido525

For the derivative of (sin-1(x))^(tan(x))

44. Dido525

@hartnn

45. hartnn

seems correct.

46. Dido525

Okay :D . Thanks!