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Learn the rule. See why it works.

Each lesson gives you a recognition pattern, a worked method, common mistakes, practice, and a direct route back to the calculator.

6 focused lessons18 practice checksRevised August 27, 2026

Lesson 1

What Is a Derivative? Meaning, Definition & Examples

Understand derivatives as slopes and instantaneous rates of change, with the limit definition, graph interpretation, examples, and practice.

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Product and Quotient Rules

Learn when to apply product and quotient rules, when to simplify first, and how to prevent sign and denominator mistakes.

Open lesson →Lesson 3

The Chain Rule

Master the chain rule for nested functions with outside-in identification, multi-layer examples, mistakes, and practice.

Open lesson →Lesson 4

Implicit Differentiation

Find dy/dx when x and y share an equation, with a four-step method, tangent slopes, and higher derivatives.

Open lesson →Lesson 5

Higher-Order Derivatives

Understand second, third, and higher derivatives, including concavity, motion, notation, and repeated differentiation.

Open lesson →Lesson 6

Trigonometric Derivatives

Learn derivatives of all six trigonometric functions, why radians matter, and how the chain rule changes them.

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Learning path

Start with meaning, then learn the patterns

Begin with what a derivative means. Continue through products, quotients, and the chain rule before moving into implicit and higher-order derivatives. Study trigonometric derivatives alongside the chain rule once the six base identities are familiar.

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