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Unit 2

2.7 Derivatives of cos x, sinx, e^x, and ln x

1 min readβ€’june 7, 2020

Sumi Vora


Derivatives of Special Functions πŸ’­

πŸŽ₯Watch: AP Calculus AB/BC - Practicing Derivative Rules
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. πŸ˜…)Β 
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(393).png?alt=media&token=e76d4203-8344-48bc-8eaf-405b78013f5e
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.Β 
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(395).png?alt=media&token=cc2853e2-ca66-4ed5-aab2-7820f5a3f7e9
The product and quotient rules are usually applied when you are taking the derivatives of special functions:Β 
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(399).png?alt=media&token=247d9751-532f-41fb-9aa3-e446a5b48742
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.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(400).png?alt=media&token=b76a95ce-b6f8-4d5d-87fa-19dfefd4a937
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(401).png?alt=media&token=1ada06d6-6c38-4930-a11f-0228b65d7271

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