Differentiation Question 1c
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:
1. Find, from the definition, the derivatives with respect to x of the following functions.
Solution: c)
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.