Differential Calculus Differentiation From First Principals using (delta x)

Ballinteer Institute {first p)

There are several ways of differentiating from first principals Method (1) uses This method works very well except when we have to show the product and quotient rules from first principals . A better way is to use and instead of h and f(x+h) . is a small change in the value of x while is a small change in the value of y ,and is the average change in y with respect to x, and the

The method involves 5 steps (1) y = f(x) (2) . (3)Take line (1) from line (2) and Simplify (4) Divide everything by (5) Let

Note as

Example 1 if Y = u.v find dy/dx from first principals

Ex 2 if y = u/v find dy/dx from first principals .

Note as above as

and . This method

and the previous method using are a lot

more straight forward than using h as

no special ' moves ' need be remembered .

Note you can differentiate all the required functions using this method it is perfectly acceptable in the exam .

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