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.

27..

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,

Using product of limits, above equation becomes,

To find the derivative

Adding and subtracting the term to the numerator of ,