Differentiation Question 1d

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.

 d)  

Answer:

d)  

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

Solution:

Putting the terms over a common denominator gives:

             

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.