Calculus is the most important ramification of mathematics. The present
and potential managers of the contemporary world make extensive uses
of this mathematical technique for making pregnant decisions. Calculus
is inevitably indispensable to measure the degree of changes relating to
different managerial issues. Calculus makes it possible for the
enthusiastic and ambitious executives to determine the relationship of
different variables on sound footings. Calculus in concerned with
dynamic situations, such as how fast production levels are increasing, or
how rapidly interest is accruing.
The term calculus is primarily related to arithmetic or probability
concept. Mathematics resolved calculus into two parts – differential
calculus and integral calculus. Calculus mainly deals with the rate of
changes in a dependent variable with respect to the corresponding
change in independent variables. Differential calculus is concerned with
the average rate of changes, whereas Integral calculus, by its very nature,
considers the total rate of changes in variables.
Differentiation is one of the most important operations in calculus. Its
theory solely depends on the concepts of limit and continuity of
functions. This operation assumes a small change in the value of
dependent variable for small change in the value of independent
variable. In fact, the techniques of differentiation of a function deal with
the rate at which the dependent variable changes with respect to the
independent variable. This rate of change is measured by a quantity
known as derivative or differential co-efficient of the function.
Differentiation is the process of finding out the derivatives of a
continuous function i.e., it is the process of finding the differential coefficient of a function.
Derivative of a Function
Bangla x sin x Pdf – The derivative of a function is its instantaneous rate of change.
Derivative is the small changes in the dependent variable with respect to
a very small change in independent variable.
Let y = f (x), derivative i.e.
dx/dy means rate of change in variable y with
respect to change in variable x.
The derivative has many applications, and is extremely useful in
optimization- that is, in making quantities as large (for example profit)
or as small (for example, average cost) as possible.
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