Join Our Discord

Learn Moreย ย ๐Ÿ‘‡

caret down
caret up
discord-logo

Join our Discord

1,000s of Fiveable Community students are already finding study help, meeting new friends, and sharing tons of opportunities among other students around the world! Don't miss out!ย  ๐ŸŽ‰

group of students
group of students

โ™พ๏ธย ap calc

ย ย >ย ย 

๐Ÿค“ย Unit 2

ย ย โ€ขย ย โฑ๏ธ1 min read

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

Sumi Vora

sumi vora

โฑ๏ธ June 7, 2020

๐Ÿ“…โŒจ๏ธ

Derivatives of Special Functions ๐Ÿ’ญ

๐ŸŽฅWatch: 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, itโ€™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. ๐Ÿ˜…)ย 

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 -- donโ€™t skip this step! Weโ€™ll discuss why we do this when we learn about the Chain Rule in Unit 3.ย 

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:ย 

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 Eulerโ€™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

A tent in the woods with a fire

Get your ap calc survival pack!

Download our ap calc survival pack and get access to every resource you need to get a 5.

ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

continue learning

Slide 1 of 12
Fiveable

Join Our Discord

discord-logo

Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students!๐ŸŽ‰

*apยฎ and advanced placementยฎ are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.

ยฉ fiveable 2021 | all rights reserved.

2550 north lake drive
suite 2
milwaukee, wi 53211