I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 3.9 : Chain Rule
4. Differentiate \(R\left( w \right) = \csc \left( {7w} \right)\) .
For this problem the outside function is (hopefully) clearly the trig function and the inside function is the stuff inside of the trig function. The derivative is then,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{R'\left( w \right) = - 7\csc \left( {7w} \right)\cot \left( {7w} \right)}}\]In dealing with functions like cosecant (or secant for that matter) be careful to make sure that the inside function gets substituted into both terms of the derivative of the outside function. One of the more common mistakes with this kind of problem is to only substitute the \(7w\) into only the cosecant or only the cotangent instead of both as it should be.