Obviously, there are a myriad of functions beyond just polynomials that we might need to take the derivatives of. These are functions that you should work on memorizing throughout the year -- you will use them quite a bit, so they should just come naturally to you after you have done a few problems. In the meantime, it’s totally okay to use a cheat sheet! (I am in Calc III and I still use a cheat sheet for some of these derivatives. 😅)
Pay attention to the du/dx at the end of every formula. This just means that you have to multiply by the derivative of u -- don’t skip this step! We’ll discuss why we do this when we learn about the Chain Rule in Unit 3.
The product and quotient rules are usually applied when you are taking the derivatives of special functions:
Another class of functions that pop up on the exam are logarithmic and exponential functions -- especially natural log and e functions. In fact, one of the definitions of Euler’s number (e) is that the derivative of e^x is also e^x.