Derivative Rules: Constant, Sum, Difference, and Constant Multiple

Abigail Young

6 min read

Next Topic - Derivatives of cos x, sinx, e^x, and ln x

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Study Guide Overview

This study guide covers derivative rules for AP Calculus AB/BC, focusing on the constant, sum, difference, and constant multiple rules. It provides formulas, examples, and practice problems for each rule, including combining them with the power rule. The guide emphasizes the importance of these foundational rules for the AP exam and offers tips for success.

#AP Calculus AB/BC: Derivative Rules - Your Ultimate Review 🚀

Hey there, future calculus masters! 👋 Let's make sure you're totally prepped for the AP exam. This guide is designed to be your best friend the night before the test—clear, concise, and super helpful. We're focusing on derivative rules today, so let's jump right in!

#2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple

These rules are your bread and butter for quickly finding derivatives of polynomial functions. Let's break them down:

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Key Concept

The Constant Rule

What it is: The derivative of any constant is always zero.
Formula: If $f(x) = c$ (where $c$ is a constant), then $f'(x) = 0$ .
Example: If $f(x) = 7$ , then $f'(x) = 0$ .

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Key Concept

The Sum Rule

What it is: The derivative of a sum of functions is the sum of their derivatives.
Formula: If $f(x) = g(x) + h(x)$ , then $f'(x) = g'(x) + h'(x)$ .
Example: If $f(x) = x^2 + 3x$ , then $f'(x) = 2x + 3$ .

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Key Concept

The Difference Rule

What it is: The derivative of a difference of functions is the difference of their derivatives.
Formula: If $f(x) = g(x) - h(x)$ , then $f'(x) = g'(x) - h'(x)$ .
Example: If $f(x) = 4x^3 - 2x$ , then $f'(x) = 12x^2 - 2$ .

#

Key Concept

The Constant Multiple Rule

What it is: T...

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Previous Topic - Applying the Power Rule Next Topic - Derivatives of cos x, sinx, e^x, and ln x

Derivative Rules: Constant, Sum, Difference, and Constant Multiple

Abigail Young

6 min read

Next Topic - Derivatives of cos x, sinx, e^x, and ln x

Listen to this study note

Study Guide Overview

#AP Calculus AB/BC: Derivative Rules - Your Ultimate Review 🚀

#2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple

These rules are your bread and butter for quickly finding derivatives of polynomial functions. Let's break them down:

#

Key Concept

The Constant Rule

What it is: The derivative of any constant is always zero.
Formula: If $f(x) = c$ (where $c$ is a constant), then $f'(x) = 0$ .
Example: If $f(x) = 7$ , then $f'(x) = 0$ .

#

Key Concept

The Sum Rule

What it is: The derivative of a sum of functions is the sum of their derivatives.
Formula: If $f(x) = g(x) + h(x)$ , then $f'(x) = g'(x) + h'(x)$ .
Example: If $f(x) = x^2 + 3x$ , then $f'(x) = 2x + 3$ .

#

Key Concept

The Difference Rule

What it is: The derivative of a difference of functions is the difference of their derivatives.
Formula: If $f(x) = g(x) - h(x)$ , then $f'(x) = g'(x) - h'(x)$ .
Example: If $f(x) = 4x^3 - 2x$ , then $f'(x) = 12x^2 - 2$ .

#

Key Concept

The Constant Multiple Rule

What it is: T...

How are we doing?

Give us your feedback and let us know how we can improve

Previous Topic - Applying the Power Rule Next Topic - Derivatives of cos x, sinx, e^x, and ln x