Differentiation Question 1e

1. Find, from the definition, the derivatives with respect to x of the following functions.

1. Find, from the definition, the derivatives with respect to x of the following functions.

Answer:

 e)

1. Find, from the definition, the derivatives with respect to x of the following functions.

Solution:

Multiplying both top and bottom by

             

             

Definition: If f is a function of x, then its derivative, i.e. its instantaneous rate of change,   is defined as

provided such limit exists. With the notation of Leibniz, if then

provided the limit exists. If is the corresponding increment in y corresponding to then

Note that, the definition of the derivative of a function is based on the concept of limit.