Q27P - Mathematical Methods in Physical Sciences

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.

 

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Step-by-Step Solution

Answer

It is proved that the derivative is,

.

Step 1: 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, .

Step 2: To write the product of functions

Let be the function.

By using the definition of differentiation,

Thus,

Using product of limits, above equation becomes,

 

Step 3: To find the derivative

Adding and subtracting the term to the numerator of ,