Question

How do you differentiate `f(x)=cot^4(3x)`?

Answer 1

The general method to differentiating compound terms is to differentiate the outside first , then the inside.
1. Differentiate exponents.
2. Differentiate the term ie `cot`
3. Differentiate any other terms within ie `(3x)`

First, differentiate `cot^4(....)`

`d/dx cot^4(....) = 4cot^3(....)`

Secondly, differentiate `cot(....)`

`d/dx cot(....) = -cosec^2(....)`
Keep in mind to retain the `3x` in the parenthesis.

Thirdly, differentiate `3x`

`d/dx 3x = 3`

Putting them all together by multiplication,

`d/dx cot^4 (3x) = 4 cot^3(3x)*(-cosec^2(3x))*3`