Lessons
Introduction to differential calculus
Derivative as slope of tangent line
Derivative as instantaneous rate of change
Secant lines
Derivative as a limit
Formal definition of derivative
Using the formal definition of derivative
Differentiability
Derivative as a function
Review: Derivative basics
Basic differentiation rules
Power rule
Polynomial functions differentiation
Rational functions differentiation (intro)
Radical functions differentiation (intro)
Sine & cosine derivatives
eˣ and ln(x) derivatives
Review: Basic differentiation
Product rule
Chain rule
Chain rule proof
Quotient rule
Review: Product, quotient, & chain rule
Rational functions differentiation
Radical functions differentiation
Trigonometric functions differentiation
Exponential functions differentiation
Logarithmic functions differentiation
Derivatives capstone
Implicit differentiation introduction
Implicit differentiation (advanced examples)
Inverse trig functions differentiation
Derivatives of inverse functions
Disguised derivatives
Proofs for the derivatives of eˣ and ln(x)
Logarithmic differentiation
Parametric & vector-valued function differentiation
Review: Advanced differentiation
Higher-order derivatives
Higher-order derivatives (parametric & vector-valued functions)
Polar curve differentiation
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.