Derivatives through first principle rule (Ab-initio method)

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"DERIVATIVES THROUGH FIRST PRINCIPLE RULE (AB-INITION METHOD):-
As we noticed in the geometrical interpretation of differentiation, we can find the derivative of a function at a given point. If the derivative exists for every point of the function, then it is defined as the derivative of the function f x.
Suppose f x is a real valued function, the function defined by
limit 'h' tending to '0' f x+h - f x / h
For this function, if the derivative exists at every point along the curve, then we say
f'(x) = limit 'h' tending to '0' f x+h - f x / h
This definition of derivative of f x is called the First Principle of Derivatives.
The function f' x or dy/dx is called the gradient function.
The process of finding the gradient value of a function at any point on the curve is called differentiation, and the gradient function is called the derivative of f x.

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