Question

How do you differentiate `f(x)=csc^3(2x)`?

Answer 1

`-6tan2xcsc^3 2x`

Explanation:

`f(x)=csc^3(2x)=(sin2x)^-3`

Now that we see the `sin2x` instead of `csc2x` term, it is pretty straight forward from here.

`(df(x))/(dx)=-3(sin2x)^-4(cos2x)(2)`
`=-6cot2xcsc^3 2x`

-The `-3` comes from the power.
-The power `-4` is because of the differentiation.
-The `cos2x` because you want to differentiate `sin2x` in the bracket.
-The `2` because you differentiate `2x`.

Cheers