We use the chain rule to unleash the derivatives of the trigonometric functions.

Up until this point of the course we have been ignoring a large class of functions: Trigonometric functions other than . We know that Armed with this fact we will discover the derivatives of all of the standard trigonometric functions.

Next we have:

Finally, we have:

The derivatives of the cotangent and cosecant are similar and left as exercises. Putting this all together, we have: