Topics
Mathematical Logic
Mathematical Logic
Matrices
Differentiation
Applications of Derivatives
Integration
Definite Integration
Applications of Definite Integration
Differential Equation and Applications
Matrices
Commission, Brokerage and Discount
Insurance and Annuity
Linear Regression
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Index Numbers
- Index Numbers
- Types of Index Numbers
- Index Numbers - Terminology and Notation
- Construction of Index Numbers
- Simple Aggregate Method
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number
Linear Programming
Assignment Problem and Sequencing
Probability Distributions
- Mean of a Random Variable
- Types of Random Variables
- Random Variables and Its Probability Distributions
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Binomial Distribution
- Bernoulli Trial
- Mean of Binomial Distribution (P.M.F.)
- Variance of Binomial Distribution (P.M.F.)
- Poisson Distribution
Continuity
Differentiation
Applications of Derivative
Indefinite Integration
Definite Integrals
Ratio, Proportion and Partnership
Commission, Brokerage and Discount
Insurance and Annuity
Demography
Bivariate Data and Correlation
Regression Analysis Introduction
Random Variable and Probability Distribution
Management Mathematics
definition
Suppose f is a real valued function and a is a point in its domain of definition. The derivative of f at a is defined by
`lim_(h -> 0 ) [ f(a+h) - f(a)]/ h`
provided this limit exists. Derivative of f (x) at a is denoted by f ′ (a).
Defination -
Suppose f is a real valued function, the function defined by
`lim_(h -> 0 ) [f(x + h) - f(x)]/h`
wherever the limit exists is defined to be the derivative of f at x and is denoted by f ′ (x). This definition of derivative is also called the first principle of derivative.
Thus f ' (x) = `lim _( h -> 0) [f( x + h) - f(x)]/h`
Clearly the domain of definition of f ′ (x) is wherever the above limit exists. There are different notations for derivative of a function. Sometimes f ′ (x) is denoted by `d/(dx) f(x)` or if y = f(x) , it is denoted by `(dy)/(dx)`. This is referred to as derivative of f(x) or y with respect to x.
It is also denoted by D (f (x) ). Further, derivative of f at x = a is also denoted by
`d/(dx) f(x) |_a` or `(df)/(dx)|_a`or even `((df)/(dx))_(x=a)`
