Question

Using the definition (2.1) of , show that the following familiar formulas hold. Hint : Use the same methods as for functions of a real variable.

26..

Short answer

It is proved that the derivative is,

.

Step-by-step solution

To write the definition (2.1) of derivative of function

The definition of the derivative of the functionis as follows:

The derivative of the function is defined as,

Where, .

To write the product of functions

Let be the function.

By using the definition of differentiation,

Thus,

To find the derivative

Adding and subtracting the term to the numerator,