EE-Learning
Differentiability and continuity
Catogry:
Math
Subject:
AP Calculus BC
Course:
Differentiation: Definition And Basic Derivative Rules
Lecture List
Product rule proof
Proof of the derivative of cos(x)
Proof of the derivative of sin(x)
Limit of (1-cos(x))/x as x approaches 0
Limit of sin(x)/x as x approaches 0
Proof of power rule for square root function
Proof of power rule for positive integer powers
Justifying the power rule
Proof: Differentiability implies continuity
Derivatives of sec(x) and csc(x)
Derivatives of tan(x) and cot(x)
Differentiating rational functions
Worked example: Quotient rule with table
Quotient rule
Worked example: Product rule with mixed implicit & explicit
Worked example: Product rule with table
Differentiating products
Product rule
Derivative of ln(x)
Derivative of 𝑒ˣ
Worked example: Derivatives of sin(x) and cos(x)
Derivatives of sin(x) and cos(x)
Tangents of polynomials
Differentiating integer powers (mixed positive and negative)
Differentiating polynomials
Basic derivative rules: table
Basic derivative rules: find the error
Basic derivative rules
Power rule (with rewriting the expression)
Power rule
Differentiability at a point: algebraic (function isn't differentiable)
Differentiability at a point: algebraic (function is differentiable)
Differentiability at a point: graphical
Differentiability and continuity
Estimating derivatives
The derivative of x² at any point using the formal definition
The derivative of x² at x=3 using the formal definition
Worked example: Derivative from limit expression
Worked example: Derivative from limit expression
Worked example: Derivative as a limit
Formal and alternate form of the derivative
Formal definition of the derivative as a limit
The derivative & tangent line equations
Derivative as slope of curve
Secant lines & average rate of change
Derivative as a concept
Newton, Leibniz, and Usain Bolt