trig differentiation (1 Viewer)

[corbs18]

How do i differentiate tan^2 dx?

 

[Pace_T]

product rule

2tanx*sec^2 (x)

 

[corbs18]

ok thanks and how do i differentiate

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

 

[acmilan]

You write that as:

tan²xtanx

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

 

[Trev]

y = tan²xtanx
dy/dx = uv' + vu'
= tan²xsec²x + tanx.2tanxsec²x
= 3tan²xsec²x

 

[rama_v]

Why are you using the product rule?

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.

 

[MuffinMan]

cant u do tanx.tanx
product rule?

 

[acmilan]

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

 

[withoutaface]

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

d/dx((cosx)^-2x - 1)
2sinx/cos³x

Possibly not the most efficient method, but interesting nonetheless.

 

[thunderdax]

Chain rule is a hell of a lot easier than product rule for these questions.