AP Calc Crash Course for Spring 2021 โ™พ๏ธ

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๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

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

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

#derivatives

#trigonometricfunctions

#exponentialfunctions

#logarithmicfunctions

#specialfunctions

โฑ๏ธย ย 1 min read

written by

Sumi Vora

sumi vora


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 

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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 

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The product and quotient rules are usually applied when you are taking the derivatives of special functions:ย 

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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

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