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# Differentiation: definition and basic derivative rules

## Defining average and instantaneous rates of change at a point

### Practice

Secant lines & average rate of changeGet 3 of 4 questions to level up!
Derivative as slope of curveGet 3 of 4 questions to level up!
The derivative & tangent line equationsGet 3 of 4 questions to level up!

## Estimating derivatives of a function at a point

### Practice

Estimate derivativesGet 3 of 4 questions to level up!

## Connecting differentiability and continuity: determining when derivatives do and do not exist

### Practice

Differentiability at a point: graphicalGet 3 of 4 questions to level up!
Differentiability at a point: algebraicGet 3 of 4 questions to level up!

## Applying the power rule

### Practice

Power rule (positive integer powers)Get 3 of 4 questions to level up!
Power rule (negative & fractional powers)Get 3 of 4 questions to level up!
Power rule (with rewriting the expression)Get 3 of 4 questions to level up!

## Derivative rules: constant, sum, difference, and constant multiple: introduction

### Practice

Basic derivative rules: find the errorGet 3 of 4 questions to level up!
Basic derivative rules: tableGet 3 of 4 questions to level up!

## Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule

### Practice

Differentiate polynomialsGet 3 of 4 questions to level up!
Tangents of polynomialsGet 3 of 4 questions to level up!

## Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)

### Practice

Derivatives of sin(x) and cos(x)Get 3 of 4 questions to level up!
Derivatives of 𝑒ˣ and ln(x)Get 5 of 7 questions to level up!

## The product rule

### Practice

Differentiate productsGet 3 of 4 questions to level up!
Product rule with tablesGet 3 of 4 questions to level up!

## The quotient rule

### Practice

Differentiate quotientsGet 3 of 4 questions to level up!
Quotient rule with tablesGet 3 of 4 questions to level up!
Differentiate rational functionsGet 3 of 4 questions to level up!

## Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions

### Practice

Derivatives of tan(x), cot(x), sec(x), and csc(x)Get 5 of 7 questions to level up!

### About this unit

The derivative of a function describes the function's instantaneous rate of change at a certain point. Another common interpretation is that the derivative gives us the slope of the line tangent to the function's graph at that point. Learn how we define the derivative using limits. Learn about a bunch of very useful rules (like the power, product, and quotient rules) that help us find derivatives quickly.