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# Unit: Differentiation: definition and basic derivative rules

AP Calc:
CHA (BI)
,
CHA‑2 (EU)
,
FUN (BI)
,
FUN‑2 (EU)
,
FUN‑3 (EU)

#### 0

Possible mastery points

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

AP Calc:
CHA (BI)
,
CHA‑2 (EU)
,
CHA‑2.A (LO)
,
CHA‑2.A.1 (EK)
,
CHA‑2.B (LO)
,
CHA‑2.B.1 (EK)
,
CHA‑2.B.2 (EK)
,
CHA‑2.B.3 (EK)
,
CHA‑2.B.4 (EK)
,
CHA‑2.C (LO)
,
CHA‑2.C.1 (EK)
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!

AP Calc:
CHA (BI)
,
CHA‑2 (EU)
,
CHA‑2.B (LO)
,
CHA‑2.B.2 (EK)
,
CHA‑2.B.3 (EK)
,
CHA‑2.B.4 (EK)
,
CHA‑2.C (LO)
,
CHA‑2.C.1 (EK)

## Estimating derivatives of a function at a point

AP Calc:
CHA (BI)
,
CHA‑2 (EU)
,
CHA‑2.D (LO)
,
CHA‑2.D.1 (EK)
Practice
Estimate derivativesGet 3 of 4 questions to level up!

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

AP Calc:
FUN (BI)
,
FUN‑2 (EU)
,
FUN‑2.A (LO)
,
FUN‑2.A.1 (EK)
,
FUN‑2.A.2 (EK)

#### Quiz 1

Level up on the above skills and collect up to 700 Mastery points

## Applying the power rule

AP Calc:
FUN (BI)
,
FUN‑3 (EU)
,
FUN‑3.A (LO)
,
FUN‑3.A.1 (EK)
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

AP Calc:
FUN (BI)
,
FUN‑3 (EU)
,
FUN‑3.A (LO)
,
FUN‑3.A.2 (EK)
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

AP Calc:
FUN (BI)
,
FUN‑3 (EU)
,
FUN‑3.A (LO)
,
FUN‑3.A.3 (EK)
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

AP Calc:
FUN (BI)
,
FUN‑3 (EU)
,
FUN‑3.A (LO)
,
FUN‑3.A.4 (EK)

AP Calc:
FUN (BI)
,
FUN‑3.A (LO)
,
FUN‑3.B (LO)
,
FUN‑3.B.1 (EK)

## The quotient rule

AP Calc:
FUN (BI)
,
FUN‑3 (EU)
,
FUN‑3.B (LO)
,
FUN‑3.B.2 (EK)
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

AP Calc:
FUN (BI)
,
FUN‑3 (EU)
,
FUN‑3.B (LO)
,
FUN‑3.B.3 (EK)
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 2300 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.
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