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Main content

Unit: Taking derivatives

About this unit

The big idea of differential calculus is the concept of the derivative, which essentially gives us the direction, or rate of change, of a function at any of its points. Learn all about derivatives and how to find them here.

Introduction to differential calculus

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Practice

Derivative as slope of curve
4 questions
Derivative & the direction of a function
4 questions

Derivative as slope of tangent line

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Practice

The derivative & tangent line equations
4 questions

Derivative as instantaneous rate of change

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Secant lines

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Practice

Secant lines & average rate of change with arbitrary points
4 questions
Secant lines & average rate of change with arbitrary points (with simplification)
4 questions

Derivative as a limit

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Practice

Derivative as a limit: numerical
4 questions

Formal definition of derivative

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Practice

Derivative as a limit
4 questions

Using the formal definition of derivative

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Differentiability

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Practice

Differentiability at a point: graphical
4 questions
Differentiability at a point: algebraic
4 questions

Derivative as a function

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Practice

Visualizing derivatives
4 questions

Review: Derivative basics

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No videos or articles available in this lesson

Practice

Derivatives basics challenge
7 questions

Basic differentiation rules

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Practice

Basic derivative rules: find the error
4 questions
Basic derivative rules: table
4 questions

Power rule

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Polynomial functions differentiation

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Practice

Differentiate polynomials
4 questions
Tangents of polynomials
4 questions

Rational functions differentiation (intro)

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Practice

Power rule (negative & fractional powers)
4 questions

Radical functions differentiation (intro)

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Practice

Power rule (with rewriting the expression)
4 questions
Differentiate integer powers (mixed positive and negative)
4 questions

Sine & cosine derivatives

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Practice

Derivatives of sin(x) and cos(x)
4 questions

eˣ and ln(x) derivatives

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Derivatives of sin(x), cos(x), tan(x), eˣ & ln(x)
(Opens a modal)

Practice

Special derivatives quiz
5 questions

Review: Basic differentiation

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No videos or articles available in this lesson

Practice

Basic differentiation challenge
7 questions
Power rule challenge
7 questions
Common derivatives challenge
7 questions

Product rule

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Practice

Differentiate products
4 questions
Product rule with tables
4 questions

Chain rule

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Practice

Chain rule intro
4 questions
Chain rule with tables
4 questions

Chain rule proof

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Quotient rule

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Practice

Differentiate quotients
4 questions
Quotient rule with tables
4 questions

Review: Product, quotient, & chain rule

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No videos or articles available in this lesson

Practice

Product, quotient, & chain rules challenge
4 questions

Rational functions differentiation

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Practice

Differentiate rational functions
4 questions

Radical functions differentiation

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Worked example: Derivative of ∜(x³+4x²+7) using the chain rule
(Opens a modal)

Practice

Differentiate radical functions
4 questions

Trigonometric functions differentiation

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Practice

Derivatives of tan(x), cot(x), sec(x), and csc(x)
7 questions
Differentiate trigonometric functions
4 questions

Exponential functions differentiation

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Practice

Derivatives of aˣ and logₐx
4 questions
Differentiate exponential functions
4 questions

Logarithmic functions differentiation

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Practice

Differentiate logarithmic functions
4 questions

Derivatives capstone

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Practice

Differentiating using multiple rules
4 questions
Tangents & normal lines challenge
4 questions

Implicit differentiation introduction

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Practice

Implicit differentiation
4 questions

Implicit differentiation (advanced examples)

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Inverse trig functions differentiation

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Derivatives of inverse functions

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Practice

Derivatives of inverse functions
4 questions

Disguised derivatives

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Disguised derivatives
(Opens a modal)

Practice

Disguised derivatives
4 questions

Proofs for the derivatives of eˣ and ln(x)

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Logarithmic differentiation

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Practice

Composite exponential function differentiation
4 questions

Parametric & vector-valued function differentiation

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Practice

Vector-valued functions differentiation
4 questions
Parametric equations differentiation
4 questions

Review: Advanced differentiation

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No videos or articles available in this lesson

Practice

Advanced differentiation challenge
4 questions

Higher-order derivatives

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Practice

Second derivatives
4 questions

Higher-order derivatives (parametric & vector-valued functions)

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Practice

Second derivatives (vector-valued functions)
4 questions
Second derivatives (parametric functions)
4 questions

Polar curve differentiation

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No videos or articles available in this lesson

Practice

Tangents to polar curves
4 questions