Mastering Derivative Rules: Simplified Guide

Michelle

12/3/2025

AP Calculus AB/BC

Derivative Rules

•

Dec 3, 2025

•

1 page

Mastering Derivative Rules: Simplified Guide

Michelle

@michylol

Calculus might seem intimidating, but derivatives are actually based on... Show more

$3.2 pules For Derivatives (:number) Ruk 1: derivative of a constant $ \frac{d}{dx} C = 0$ ex. f(x)=3 Rule 2: Power Rule f(x)= ax^n f'(x$

Rules for Derivatives

Finding derivatives becomes much easier when you know the basic rules. Let's break them down:

Rule 1: Derivative of a constant is always zero. If f(x) = 3, then f'(x) = 0. Constants don't change as x changes, so their rate of change is zero!

Rule 2: Power Rule states that if f(x) = ax^n, then f'(x) = n·ax^ $n-1$ . This rule is super useful - you multiply by the power and then reduce the power by 1. For example, the derivative of x^4 is 4x^3.

Rule 3: Constant Multiple Rule lets you pull constants outside the derivative. For f(x) = 3x², f'(x) = 3(2x) = 6x.

Rule 4: Sum Rule means you can find derivatives term by term. For f(x) = x⁴ + 12x², f'(x) = 4x³ + 24x.

Rule 5: Product Rule helps when multiplying functions. If f(x) = u·v, then f'(x) = (u·dv) + (v·du). For example, with f(x) = $2x-5$ $3x+2$ , f'(x) = $2x-5$ (3) + $3x+2$ (2).

Remember This! The Product Rule follows the pattern "first times derivative of second, plus second times derivative of first."

Rule 6: Quotient Rule works for fractions. If f(x) = u/v, then f'(x) = $v·du - u·dv$ /v². Think "low d-high minus high d-low, over low squared."

Rule 7: Power Rule for Negative Exponents works just like the regular power rule. For f(x) = 2x^(-3), f'(x) = -6x^(-4).

The exponential function has a special property: the derivative of e^x is e^x - it's its own derivative!

Second derivatives (f"(x)) are just the derivatives of the first derivatives. They measure how the rate of change is itself changing.

We thought you’d never ask...

What is the Knowunity AI companion?

Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.

Where can I download the Knowunity app?

You can download the app in the Google Play Store and in the Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

Elisha

iOS user

Paul T

iOS user

AP Calculus AB/BC

•

Dec 3, 2025

•

1 page

Mastering Derivative Rules: Simplified Guide

Michelle

@michylol

Calculus might seem intimidating, but derivatives are actually based on straightforward rules that follow patterns. This summary covers the essential rules for finding derivatives, which are fundamental tools for analyzing how functions change.

$3.2 pules For Derivatives (:number) Ruk 1: derivative of a constant $ \frac{d}{dx} C = 0$ ex. f(x)=3 Rule 2: Power Rule f(x)= ax^n f'(x$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Rules for Derivatives

Finding derivatives becomes much easier when you know the basic rules. Let's break them down:

Rule 1: Derivative of a constant is always zero. If f(x) = 3, then f'(x) = 0. Constants don't change as x changes, so their rate of change is zero!

Rule 3: Constant Multiple Rule lets you pull constants outside the derivative. For f(x) = 3x², f'(x) = 3(2x) = 6x.

Rule 4: Sum Rule means you can find derivatives term by term. For f(x) = x⁴ + 12x², f'(x) = 4x³ + 24x.

Rule 5: Product Rule helps when multiplying functions. If f(x) = u·v, then f'(x) = (u·dv) + (v·du). For example, with f(x) = $2x-5$ $3x+2$ , f'(x) = $2x-5$ (3) + $3x+2$ (2).

Remember This! The Product Rule follows the pattern "first times derivative of second, plus second times derivative of first."

Rule 6: Quotient Rule works for fractions. If f(x) = u/v, then f'(x) = $v·du - u·dv$ /v². Think "low d-high minus high d-low, over low squared."

Rule 7: Power Rule for Negative Exponents works just like the regular power rule. For f(x) = 2x^(-3), f'(x) = -6x^(-4).

The exponential function has a special property: the derivative of e^x is e^x - it's its own derivative!

Second derivatives (f"(x)) are just the derivatives of the first derivatives. They measure how the rate of change is itself changing.