TOC
Courses
Blog
Twitch
Shop
Search
Search subtopics
Search all
Toggle menu
Courses
Blog
Subreddit
Discord
Log in
Sign up
▾
Calculus 1
▸
Limits and continuity
•
Intro to calc 1
•
Estimating limits from graphs
•
Estimating limits from tables
•
Intro to continuity
•
Finding and classifying discontinuities
•
Finding the value that makes the function continuous
▸
Derivatives: definition and basic derivative rules
•
Proving differentiable implies continuous
•
Derivative of a function from first principles
•
Finding the tangent or normal line through the given point
•
Constant rule
•
Constant multiple rule for derivatives
•
Sum, difference, and power rules for derivatives
•
Product rule
•
Proving the product rule
•
Quotient rule
•
Derivatives of trig functions
•
Proving properties of even and odd functions (calculus 1)
•
Leibniz's derivative notation
•
Logarithmic functions
▸
Derivatives: composite, implicit, and inverse functions
•
Derivative at a point from first principles
•
Derivatives of exponential functions
•
Derivatives of logarithmic functions
▸
Derivatives of hyperbolic and inverse hyperbolic functions
•
Using the derivatives of the hyperbolic functions
•
Proving the derivatives of the hyperbolic functions
•
Proving the derivatives of the inverse hyperbolic functions
•
Derivatives of inverse trig functions
•
Derivatives of transcendental functions
•
Derivatives of trigonometric functions under transformations
•
Derivative using u-substitution
•
Determining derivatives from graphs
•
Higher order derivatives
•
Chain rule
•
Derivatives of inverse functions
•
Choosing the derivative rules to use
▸
Applying derivatives to analyze functions
•
Applications of trigonometric derivatives
•
Extreme value theorem
•
First derivative test
•
Mean value theorem
▸
Monotonic intervals and functions
•
Intro
•
Proofs
•
Related rates
•
Second derivative test
•
Concavity
•
Factoring a cubic polynomial with a double root
•
Graphing using derivatives
▸
Special points
▸
Finding critical values from graphs
•
Lesson
•
Practice
•
Finding critical values using derivatives
▸
Inflection points
•
Graphically finding points of inflection
•
Using the second derivative to find points of inflection
•
Classifying stationary points
•
Sketching polynomials using stationary points
•
Bisection method
•
Newton's method
•
False position method
•
L'Hopital's rule
▸
Integrals
•
Basic integration problems
▸
Integration by u-substitution
▸
Integration by u-substitution (less difficult)
•
Lesson
•
Practice
•
Integration by u-substitution (more difficult)
•
Integrating exponential functions by u-substitution
•
Visually determining antiderivative
▸
Applications of integrals
•
Proving the formula for the area of a circle
•
Area between two curves
▸
Solids of revolution
•
Disc and washer methods (circular cross sections)
•
Volumes of solids with known cross sections
•
Shell method
•
Volume of a sphere (calculus \(2\))
•
Volume of a cone (calculus 2)
›
Calculus 1
Applying derivatives to analyze functions
Applications of trigonometric derivatives
Extreme value theorem
First derivative test
Mean value theorem
Monotonic intervals and functions
Related rates
Second derivative test
Concavity
Factoring a cubic polynomial with a double root
Graphing using derivatives
Special points
Bisection method
Newton's method
False position method
L'Hopital's rule
Other resources