# Derivative or Differential Coefficient of a Function.

Differential calculus or the concept of Derivative and Differential Coefficient was discovered by Isaac Newton (1642-1727) and Gottfried Wilhelm Leibnitz (1646-1716) in the process of solving two old problems one of finding slope of tangent drawn to a curve and another of finding instantaneous velocity of an object in non-uniform motion.

**Derivative: **

When a variable** **“y” is defined as a function** **of another variable “x” or,

f(x)=y

Then , The Derivative or Differential Coefficient of the function “f” at a point “x” or with respect to “x” is the limiting value of:

The derivative of a function of “x” with respect to “x” is denoted by:

for example:

If “y” is a function of “x” or f(x)=y whose graph looks like:

Then the derivative of the function “f” with respect to “x” at point “x” is :-

which can be shown in figure as:

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