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Dido525

  • 2 years ago

Find the derivative:

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  1. Dido525
    • 2 years ago
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    |dw:1349927470125:dw|

  2. Dido525
    • 2 years ago
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    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
    • 2 years ago
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    i think it will be better to take the log of that part with the respect of e base.

  4. Dido525
    • 2 years ago
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    |dw:1349927833215:dw|

  5. sritama
    • 2 years ago
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    |dw:1349927846691:dw|

  6. sritama
    • 2 years ago
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    yeah.

  7. Dido525
    • 2 years ago
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    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
    • 2 years ago
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    Like I thought you had to take the log of both sides for logarithmic differentiation.

  9. sritama
    • 2 years ago
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    yes,or you may solve the two parts one by one

  10. Dido525
    • 2 years ago
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    So I thought you had to:|dw:1349927977970:dw|

  11. Dido525
    • 2 years ago
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    Do you do that?

  12. Dido525
    • 2 years ago
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    Don't*

  13. sritama
    • 2 years ago
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    and even if you take the ln of ln(x+ln(x+ln(x))),there ain't any problem

  14. Dido525
    • 2 years ago
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    Yes yes. I knew that. But is that valid? I though you had to Log both sides of the ENTIRE term.

  15. Dido525
    • 2 years ago
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    Ohh? Why not?

  16. sritama
    • 2 years ago
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    yes it is.

  17. Dido525
    • 2 years ago
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    How is it valid? Sorry for being stubborn.

  18. hartnn
    • 2 years ago
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    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
    • 2 years ago
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    Ohh I know @hartnn . I didn't seperate it.

  20. sritama
    • 2 years ago
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    |dw:1349928327564:dw|

  21. sritama
    • 2 years ago
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    that is why you can find the derivatives separately

  22. Dido525
    • 2 years ago
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    Lol I know. By I mean why can you ln only the (arcsin)^Tan(x)? I though you had to ln EVERYTHING.

  23. hartnn
    • 2 years ago
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    "had to" <---no

  24. sritama
    • 2 years ago
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    why?? if you solve them part by part, you are free to take the ln of one part without changing the other

  25. Dido525
    • 2 years ago
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    Ohh. Okay. That explains it.

  26. Dido525
    • 2 years ago
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    Fair enough haha...

  27. Dido525
    • 2 years ago
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    Could I do this instead? |dw:1349928628192:dw|

  28. Dido525
    • 2 years ago
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    For the derivative I mean.

  29. Dido525
    • 2 years ago
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    @sritama ,@hartnn

  30. Dido525
    • 2 years ago
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    @hartnn

  31. hartnn
    • 2 years ago
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    NO! what have u done!!

  32. sritama
    • 2 years ago
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    i couldn't get it @Dido525 :(

  33. Dido525
    • 2 years ago
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    You make me chukle @hartnn .

  34. sritama
    • 2 years ago
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    how and why will you do that?

  35. Dido525
    • 2 years ago
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    Well the derivative of a^x = a^x *ln(a)

  36. hartnn
    • 2 years ago
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    ln y = tan x ln(sin^-1 (x)) diff. this. no other way

  37. Dido525
    • 2 years ago
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    Okay okay :P .

  38. Dido525
    • 2 years ago
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    Then this question isn't so hard.

  39. hartnn
    • 2 years ago
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    is it ? what u get as y' ?

  40. Dido525
    • 2 years ago
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    Wait.

  41. Dido525
    • 2 years ago
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    Doing it now.

  42. Dido525
    • 2 years ago
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    I got: |dw:1349929346410:dw|

  43. Dido525
    • 2 years ago
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    For the derivative of (sin-1(x))^(tan(x))

  44. Dido525
    • 2 years ago
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    @hartnn

  45. hartnn
    • 2 years ago
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    seems correct.

  46. Dido525
    • 2 years ago
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    Okay :D . Thanks!

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