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

1 Answer
Jun 13, 2017

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