differentiation of log x


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Logarithmic Differentiation
Logarithmic Differentiation - When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation.When we want to differentiate a function of the form f(x) g(x), we use..
Logarithmic Differentiation
When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation. Let y = f(x) g(x) Taking log on both sides, we have logy = g(x) logf(x). ..
Differentiability
We have already defined the derivative of a function f(x) at a particular point 'a' and derivative of f(x) in general for the variable x as f'(a) and f'(x) respectively. The restriction in both the cases is that 'the limit must exist'. If does n..
Differentiability
>does not exist, then we say that the function is not differentiable. If the above limit exists, we say the function f(x) is differentiable. In order to test the differentiability of a function at a point, the right hand derivative and left hand derivatives a..
Logarithmic Series
If x is a real number such that |x|<1, then the series is called the logarithmic series. It can be proved mathematically that this logarithmic series has the sum equal to log(1 + x). If x is a real number such that |xh..
Logarithmic Series
If x is a real number such that |x|<1, then the series is called the logarithmic series. It can be proved mathematically that this logarithmic series has the sum equal to log(1 + x..
Graph of Logarithmic Series
We see that as x increases from 0 to , the value of log x also increases indefinitely. The function log x is one-on..
Graph of Logarithmic Function
For x (0, ), the value of log x is uniquely defined.For x (0, ), the value of log x is uniquely defined. \ x g log x is a well-defined function from (0, ) to (- , ). The value of e to one place of decimal i..
Particular Logarithmic Series
For any number x such that |x|<1. i) For number x:|x|<1, we have |-x|=|x|<1. iii) It can be proved mathematically that the logarithmic series (1) is true even when x=1..
Exponential and Logarithmic Series
The sum of the infinite series 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... is called the exponential number. If x is any complex number then the series is called the exponential series. It can be proved mathematically that this exponential series has a sum and we denote it by e ..
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