anonymous
  • anonymous
How can I find the derivative of tan(5/x) ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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IrishBoy123
  • IrishBoy123
if you know the derivative of tan u and the derivative of 5/x, you can use the chain rule.
IrishBoy123
  • IrishBoy123
by letting u = 5/x
anonymous
  • anonymous
I don't know the derivative of tan u xD Is there any way to find it without having it memorized?

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SolomonZelman
  • SolomonZelman
no need for u
IrishBoy123
  • IrishBoy123
it's a really good one to know, especially for integration
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan(x/5)~\right) }\)
SolomonZelman
  • SolomonZelman
how would you differentiate if it was just tan(x) ?
anonymous
  • anonymous
I don't know lol I get confused when it comes to tan
SolomonZelman
  • SolomonZelman
what is the derivative of tan(x), you don't know ?
anonymous
  • anonymous
Nope xD
SolomonZelman
  • SolomonZelman
you can use a quotient rule, do you know what a quotient rule is?
IrishBoy123
  • IrishBoy123
@Tracy96 cheers
SolomonZelman
  • SolomonZelman
Do you know what d/dx means ?
anonymous
  • anonymous
Ohhh now I remember it was sec^2x hahaha
anonymous
  • anonymous
Working on math too much today XD lol
SolomonZelman
  • SolomonZelman
yes, derivative of tan(x) is sec^2(x)
SolomonZelman
  • SolomonZelman
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)
SolomonZelman
  • SolomonZelman
For example, \(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan (4x)~\right)=\sec^2(4x)\times \left(\frac{d}{dx}~4x\right) }\) \(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan (4x)~\right)=\sec^2(4x)\times ~4 }\) \(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan (4x)~\right)=4\sec^2(4x) }\)
anonymous
  • anonymous
Ok so that will be \[\sec^2(5/x)(\frac{ -5 }{ x^2 })\]
SolomonZelman
  • SolomonZelman
yes, that is correct, but I would put the last part in front to avoid any confusion
SolomonZelman
  • SolomonZelman
confusion*
anonymous
  • anonymous
Right! Thanks so much @SolomonZelman :D
SolomonZelman
  • SolomonZelman
Sure. Any questions you have regarding this problem or any of the rules?
anonymous
  • anonymous
Nope! Thanks! That was very helpful :)
SolomonZelman
  • SolomonZelman
Alright. You are always welcome!
anonymous
  • anonymous
:)

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