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anonymous
 one year ago
How can I find the derivative of tan(5/x) ?
anonymous
 one year ago
How can I find the derivative of tan(5/x) ?

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IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1if you know the derivative of tan u and the derivative of 5/x, you can use the chain rule.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1by letting u = 5/x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't know the derivative of tan u xD Is there any way to find it without having it memorized?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1it's a really good one to know, especially for integration

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0\(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan(x/5)~\right) }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0how would you differentiate if it was just tan(x) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't know lol I get confused when it comes to tan

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0what is the derivative of tan(x), you don't know ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0you can use a quotient rule, do you know what a quotient rule is?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Do you know what d/dx means ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhh now I remember it was sec^2x hahaha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Working on math too much today XD lol

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, derivative of tan(x) is sec^2(x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0And 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
 one year ago
Best ResponseYou've already chosen the best response.0For 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
 one year ago
Best ResponseYou've already chosen the best response.0Ok so that will be \[\sec^2(5/x)(\frac{ 5 }{ x^2 })\]

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, that is correct, but I would put the last part in front to avoid any confusion

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right! Thanks so much @SolomonZelman :D

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Sure. Any questions you have regarding this problem or any of the rules?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nope! Thanks! That was very helpful :)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Alright. You are always welcome!
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