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CONTENT

1. Meaning of differentiation/derived function.
2. Differentiation from the first principle.
3. Standard derivatives of some basic functions.

MEANING OF DIFFERENTIATION/DERIVED FUNCTION

The process of finding the differential coefficient of a function is called differentiation. Differentiation deals with the measure of the rate of change in a particular function when some quantities in the function is either increased or decreased. For example, given the function $$y = f(x)$$, a change in $$x$$ will produce a corresponding change in $$y$$. When $$y$$ is increased, $$x$$ is bound to increase in proportion and vice versa. Note: The reverse of differentiation is integration.

DIFFERENTIATION FROM THE FIRST PRINCIPLE

The method of finding the derivative of a function from definition is called differentiation from the first principle.  Note: A change in $$x$$ to  $$x + Δx$$ produces a corresponding change in $$y$$  to $$y + Δy$$.

Example 1:

Differentiate the following from the first principle

(a) $$y = 2x + 5$$

(b) $$y = x^2$$

SOLUTION

(a) $$y = 2x + 5$$

Take increment in both $$x$$ and $$y$$.

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