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anonymous

  • one year ago

How can I find the derivative of tan(5/x) ?

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  1. IrishBoy123
    • one year ago
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    if you know the derivative of tan u and the derivative of 5/x, you can use the chain rule.

  2. IrishBoy123
    • one year ago
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    by letting u = 5/x

  3. anonymous
    • one year ago
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    I don't know the derivative of tan u xD Is there any way to find it without having it memorized?

  4. SolomonZelman
    • one year ago
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    no need for u

  5. IrishBoy123
    • one year ago
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    it's a really good one to know, especially for integration

  6. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan(x/5)~\right) }\)

  7. SolomonZelman
    • one year ago
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    how would you differentiate if it was just tan(x) ?

  8. anonymous
    • one year ago
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    I don't know lol I get confused when it comes to tan

  9. SolomonZelman
    • one year ago
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    what is the derivative of tan(x), you don't know ?

  10. anonymous
    • one year ago
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    Nope xD

  11. SolomonZelman
    • one year ago
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    you can use a quotient rule, do you know what a quotient rule is?

  12. IrishBoy123
    • one year ago
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    @Tracy96 cheers

  13. SolomonZelman
    • one year ago
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    Do you know what d/dx means ?

  14. anonymous
    • one year ago
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    Ohhh now I remember it was sec^2x hahaha

  15. anonymous
    • one year ago
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    Working on math too much today XD lol

  16. SolomonZelman
    • one year ago
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    yes, derivative of tan(x) is sec^2(x)

  17. SolomonZelman
    • one year ago
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    And when you have tan(x/5) the only difference is that it is sec^2( x/5 ), AND you need to multiply that times the chain rule..... (chain rule for x/5)

  18. SolomonZelman
    • one year ago
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    For example, \(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan (4x)~\right)=\sec^2(4x)\times \left(\frac{d}{dx}~4x\right) }\) \(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan (4x)~\right)=\sec^2(4x)\times ~4 }\) \(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan (4x)~\right)=4\sec^2(4x) }\)

  19. anonymous
    • one year ago
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    Ok so that will be \[\sec^2(5/x)(\frac{ -5 }{ x^2 })\]

  20. SolomonZelman
    • one year ago
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    yes, that is correct, but I would put the last part in front to avoid any confusion

  21. SolomonZelman
    • one year ago
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    confusion*

  22. anonymous
    • one year ago
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    Right! Thanks so much @SolomonZelman :D

  23. SolomonZelman
    • one year ago
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    Sure. Any questions you have regarding this problem or any of the rules?

  24. anonymous
    • one year ago
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    Nope! Thanks! That was very helpful :)

  25. SolomonZelman
    • one year ago
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    Alright. You are always welcome!

  26. anonymous
    • one year ago
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    :)

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