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Differentiation

Derivative of a Function Using First Principle

• Suppose f is a real-valued function and a is a point in the domain of definition. If the limit exists, then it is called the derivative of f at a. The derivative of f at a is denoted by.

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• Suppose f is a real-valued function. The derivative of f {denoted by or } is defined by

This definition of derivative is called the first principle of derivative.
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• For example, the derivative of is calculated as follows.
We have; using the first principle of derivative, we obtain

Solved Examples

Example 1:
Find the derivative of f(x…

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