Question

What is the derivative of csc(3x)?

Answer 1

I'll add some detail: how you get there.

Explanation:

...you use the rule for finding the derivative of the quotient of 2 functions.

If `f(x) = (g(x))/(h(x)), then f'(x) = (g'(x)h(x) - g(x)h'(x))/(h(x)^2)`

So, you start by rewriting `csc(3x) = 1/sin(3x)`

Here, g(x) = 1, g'(x) = 0, h(x) = sin(3x), h'(x) = 3cos(3x)

Put all this together:

`d/dx(1/sin(3x)) = (-3cos(3x))/(sin^2(3x))`

`= (-3cos(3x))/(sin(3x)sin(3x))`

`=-3cot(3x)csc(3x)`

GOOD LUCK