Functions Contents - F
Differential calculus
Differential Calculus - Derivatives and differentials
The derivative of a function
Tangent to a curve
The equation of the line tangent to the given curve at the given point
Determining the lines tangent to the graph of a function from a point outside the function
lines tangent to the graph of a function from a point outside the function example
The derivative as a function
Derivatives of basic or elementary functions
Differentiation rules
The derivative of the sum or difference of two functions
A constant times a function rule
The quotient rule
Table of derivatives of elementary functions
The chain rule applications
Implicit differentiation
Implicit differentiation examples
Generalized power rule
Generalized power rule examples
Logarithmic differentiation
Logarithmic differentiation examples
Derivative of a composite exponential function
Use of the logarithmic differentiation
Derivatives of composite functions examples
Derivatives of the hyperbolic functions
Derivatives of inverse hyperbolic functions
Derivative of the inverse function
Derivatives of the inverse trigonometric functions
Derivative of parametric functions, parametric derivatives
Derivative of parametric functions example
Derivative of vector-valued functions
Applications of the derivative
Tangent, normal, subtangent and subnormal
Property of the parabola
Property of power functions
Property of the exponential function

Angle between two curves examples
Differential of a function
Use of differential to approximate the value of a function
Rules for differentials
Differentials of some basic functions

Increasing/decreasing test

Concave up and concave down definition
Points of inflection
Points of inflection and concavity of the sine function
Points of inflection and concavity of the cubic polynomial
Approximate solution to an equation, Newton's method (or the Newton-Raphson method)

Maclaurin's formula or Maclaurin's theorem

Properties of the power series expansion of the exponential function

Properties of the power series expansion of the sine function
Extreme points, local (or relative) maximum and local minimum
The first derivative test
The second derivative test and concavity
Finding and classifying critical or stationary points
Finding extreme points
Points of inflection
Finding points of inflection
Finding and classifying critical or stationary points examples