Question

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

Answer 1

if you know the derivative of tan u and the derivative of 5/x, you can use the chain rule.

Answer 2

by letting u = 5/x

Answer 3

I don't know the derivative of tan u xD Is there any way to find it without having it memorized?

Answer 4

no need for u

Answer 5

it's a really good one to know, especially for integration

Answer 6

\(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan(x/5)~\right) }\)

Answer 7

how would you differentiate if it was just tan(x) ?

Answer 8

I don't know lol I get confused when it comes to tan

Answer 9

what is the derivative of tan(x), you don't know ?

Answer 10

Nope xD

Answer 11

you can use a quotient rule, do you know what a quotient rule is?

Answer 12

@Tracy96

cheers

Answer 13

Do you know what d/dx means ?

Answer 14

Ohhh now I remember it was sec^2x hahaha

Answer 15

Working on math too much today XD lol

Answer 16

yes, derivative of tan(x) is sec^2(x)

Answer 17

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)

Answer 18

For example,

\(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan (4x)~\right)=\sec^2(4x)\times \left(\frac{d}{dx}~4x\right) }\)

\(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan (4x)~\right)=\sec^2(4x)\times ~4 }\)

\(\large\color{black}{ \displaystyle \frac{d}{dx}\left(~\tan (4x)~\right)=4\sec^2(4x) }\)

Answer 19

Ok so that will be \[\sec^2(5/x)(\frac{ -5 }{ x^2 })\]

Answer 20

yes, that is correct, but I would put the last part in front to avoid any confusion

Answer 21

confusion*

Answer 22

Right! Thanks so much @SolomonZelman :D

Answer 23

Sure. Any questions you have regarding this problem or any of the rules?

Answer 24

Nope! Thanks! That was very helpful :)

Answer 25

Alright. You are always welcome!

Answer 26

:)