Find the derivative of 1/(-sint)?

I've taken the negative sign out to get $- \left(\frac{1}{\setminus} \sin t\right) '$ but that's as far as I got... I wanted to apply the product rule instead of the quotient rule. (Symbolab uses the quotient rule)

May 28, 2018

$\cot \left(t\right) \csc \left(t\right)$

Explanation:

Before starting we know that
$- \frac{1}{\sin} t = - \csc t$

Also

$- \frac{d}{\mathrm{dt}} \csc t = - \left(- \cot \left(t\right) \csc \left(t\right)\right)$

$= \cot \left(t\right) \csc \left(t\right)$