trig differentiation (1 Viewer)

corbs18

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ok thanks and how do i differentiate

tan(cubed) dx
or
tan^3 dx
???
as long as u kno wat im talkin bout
 

acmilan

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You write that as:

tan2xtanx

and then use the product rule again, knowing what the derivative of tan2x is
 

rama_v

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Slide Rule said:
Why are you using the product rule? :p

Function of a function rule:
tan^3(x)=(tanx)^3
let u=tanx
so derivative is 3u'.u^2=3sec^2(x)tan^2(x)

You can do it in your head, though. E.g. tan^4(x) derivative is 4sec^2(x)tan^3(x).
Yep, thats clearly the better method esppecially when dealing with negative powers.
 

acmilan

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For tan2x its not a huge difference but when you get to other powers product rule gets annoying
 

withoutaface

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tan2x = (1-cos2x)/cos2x = (cosx)-2- 1

d/dx((cosx)-2x - 1)
2sinx/cos3x

Possibly not the most efficient method, but interesting nonetheless.
 

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