Question

How do you differentiate `f(x)=cscx` using the quotient rule?

Answer 1

First we must write `f(x)` as a quotient.

Explanation:

`f(x) = cscx = 1/sinx`

Now use the quotient rule to differentiate:

`f'(x) = ((0)(sinx)-(1)(cosx))/(sinx)^2`

`= -cosx/sin^2x`

`= -cosx/sinx 1/sinx`

`= -cotx cscx = -cscx cotx`

(Choose a way of expressing the answer that you (or your grader) prefer.)