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loge(x)
The derivative of the function/ loge(x)

Derivative of loge(x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 log(x)
-------
   / 1\
log\e /
log⁡(x)log⁡(e1)\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}} 
log(x)/log(exp(1))
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

    So, the result is: 1xlog⁡(e1)\frac{1}{x \log{\left(e^{1} \right)}}

  2. Now simplify:

    1x\frac{1}{x}

The answer is:

1x\frac{1}{x}

The graph
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    1    
---------
     / 1\
x*log\e /
1xlog⁡(e1)\frac{1}{x \log{\left(e^{1} \right)}}
Simplify
The second derivative [src] 
   -1     
----------
 2    / 1\
x *log\e /
−1x2log⁡(e1)- \frac{1}{x^{2} \log{\left(e^{1} \right)}}
Simplify
The third derivative [src] 
    2     
----------
 3    / 1\
x *log\e /
2x3log⁡(e1)\frac{2}{x^{3} \log{\left(e^{1} \right)}}
Simplify
The graph
Derivative of loge(x)
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