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

Benjamin Wright
6 min read
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Study Guide Overview
This study guide covers derivatives of special functions, including sin(x), cos(x), eˣ, and ln(x). It provides a quick reference table of these derivatives, examples of how to apply them, common mistakes to avoid, and practice questions. The guide emphasizes memorizing the derivatives, combining them with other derivative rules (like the chain rule), and applying them in the context of AP exam questions.
#Derivatives of Special Functions: Your Cheat Sheet 🚀
Hey there! Let's dive into the derivatives of those special functions you'll see all the time: , , , and . The good news? Once you memorize these rules, they're super straightforward! This guide is designed to make sure you're ready to nail these on the AP exam. Let's get started!
#Quick Reference Table
Here's a handy table summarizing the derivatives of these special functions. Keep this close – it's your secret weapon! 😉
Function | Derivative |
---|---|
Memorize these! They’re the building blocks for more complex problems. Use the mnemonic "Sine goes to Cosine" (and remember the negative for cosine) to help you remember.
#Derivative of
The derivative of is always . Simple as that! Let's see it in action:
#Example:
To find , we take the derivative of each term separately:
- The derivative of
4\sin x
is4\cos x
(since the derivative of is ). - The derivative of
3x
is3
(using the power rule).
So, .
Remember to apply the constant multiple rule when a function...

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