General Exponential functions- Defn and properties

1. General Exponential Functions
BSC MATHEMATICS
SEMESTER III
MODULE I
CHAPTER 6 SECTION 4
UNIVERISTY OF CALICUT

2. We will now consider exponential functions that have bases other than e . To define these
functions, recall that

3. Therefore, if a is a positive real number,

4. Remark:
We had proved that ln x r = r ln x, if r is a rational number
Now, by defn of general exp. fn, ay = ey ln a , for every real y.
Therefore, ln ay = ln ey ln a = y ln a , for every real y.
ln ay = y ln a, for every real number y.

12. The power function is differentiated by using the Power Rule.
The derivative of the exponential function is found by using
the rule for differentiating such functions
In case both the base and the exponent are functions of, is
differentiated by using logarithmic differentiation
BeCareful!!

16. THANK YOU ! !