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# Unit: Derivatives: definition and basic rules

#### 0

Possible mastery points

## Average vs. instantaneous rate of change

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

Practice
Estimate derivativesGet 3 of 4 questions to level up!

## Differentiability

#### Quiz 1

Level up on the above skills and collect up to 900 Mastery points

## 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

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!

## Combining the power rule with other derivative rules

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

#### Quiz 2

Level up on the above skills and collect up to 800 Mastery points

## 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!

## Derivatives of tan(x), cot(x), sec(x), and csc(x)

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

#### Quiz 3

Level up on the above skills and collect up to 800 Mastery points
Up next for you:

#### Unit test

Level up on all the skills in this unit and collect up to 2500 Mastery points!

### 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.