---
title: "Derivation Rules & Examples"
description: "Differentiate f(x) = 3x² + 2x + 5 one term at a time with the constant, sum and power rules, then use the product rule when two changing terms multiply."
canonical_url: "https://fanout.sh/ai/lessons/math-fundamentals-derivation-rules"
md_url: "https://fanout.sh/ai/lessons/math-fundamentals-derivation-rules.md"
access: "pro-preview"
---

# Derivation Rules & Examples

Differentiate f(x) = 3x² + 2x + 5 one term at a time with the constant, sum and power rules, then use the product rule when two changing terms multiply.

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- Module: Math Fundamentals

## A glimpse of Derivation Rules & Examples

Suppose a score depends on a number x through f(x) = 3x² + 2x + 5. You want its local rate of change: if x moves a little, how quickly does the score move?

That rate is the derivative, written f′(x). We can calculate it one term at a time.

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