4.12 Derivatives of Exponential and Logarithmic Functions
The number ‘ e ’
![](Image323.gif)
Therefore the limit of ,
as n approaches infinity is ![](Image324.gif)
The number defined by ![](Image326.gif) , or by the sum of the convergent series , is denoted by ‘ e ’. Its value, correct to 6 decimal places is 2 . 718282 i.e. clearly 2 < e < 3. It is also a fundamental constant like p and it is the
base of the natural or Napierian, or hyperbolic, logarithms.
The exponential function ex which is sometimes written as
e x p x is ![](Image327.gif)
Another important function is ![](Image328.gif)
* Exponential functions in which a variable quantity occurs as
an index, or exponent.
The function are examples of exponential functions.
Now , let y = f ( x ) = ex then f ( x + h ) = e x + h
= ex . eh
Then by the 1st principal of derivatives we get ![](Image330.gif)
Differentiation of ![](Image331.gif)
Differentiation of ‘log x’:-
Let y = logyex i.e. f ( x ) = log x Þ f ( x + h ) = log ( x + h )
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