DerivCalc
Learning center

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 core lessons + 4 focused resources28+ practice checksRevised September 23, 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.

Open lesson →Lesson 2

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.

Open lesson →
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.

Every calculator result names its rules, so you can move between a live result and the matching lesson. For a particular expression, browse the worked-solutions library.

Focused practice and printable references

Interactive rule calculators

Use these focused calculators when you know the likely rule and want a complete lesson beside the result.

How the library is maintained

SilverCodeLabs writes and maintains these lessons. Examples are checked symbolically and numerically, revision dates are displayed, and every lesson links to a standard calculus reference. See the methodology and limitations.