Topic 1: Further Differentiation and Applications
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Derivatives of exponential functions – An introduction
Derivatives of exponential functions Simple rules
Applications of derivatives of exponential Functions
Derivatives of periodic functions 1 A graphical explanation
Derivatives of Periodic functions 2 Simple examples
Derivatives of periodic functions Applications 1
Derivatives of periodic functions Applications 2
Derivatives of polynomials, negative and fractional powers by rule
Composite functions and the chain rule
The chain rule the fast way
The product rule
The quotient rule
The chain rule revisited
The Product Rule Revisited
Concave up and Concave down Part 1: 2 useful definitions
Concavity and the second derivative
Points of Inflection and the 2nd derivative
The 2nd Derivative test
Sketching Functions with the second derivative and Points of Inflection
Introduction to Kinematics
Applications of Integration in motion questions
Optimisation when the function is unknown
Topic 2: Integrals
Intro to Integration and integrating polynomials
Integration a little bit of theory
Integration finding the c value
Integration the reverse chain rule
Integration resulting in a logarithm
Integrals of exponentials
Integration of trig functions
Integration by recognition updated
Applications of Integration in motion questions
The definite integral
The definite integral signed area
Area between two curves
The area under a derivative function
Trapezoidal Rule Fully explained
Topic 3: Discrete Random Variables
Discrete Random Variables
Discrete Random Distributions Expected value
Probability Distributions Discrete vs continuous random variables
Discrete Probability distributions 2 Properties of discrete probability distributions