Derivative of loge(x)

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 log(x)
-------
   / 1\
log\e /

$$\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}$$

log(x)/log(exp(1))

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
So, the result is: $\frac{1}{x \log{\left(e^{1} \right)}}$
Now simplify:

$\frac{1}{x}$

The answer is:

$\frac{1}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    1    
---------
     / 1\
x*log\e /

$$\frac{1}{x \log{\left(e^{1} \right)}}$$

Simplify

The second derivative [src]

   -1     
----------
 2    / 1\
x *log\e /

$$- \frac{1}{x^{2} \log{\left(e^{1} \right)}}$$

Simplify

The third derivative [src]

    2     
----------
 3    / 1\
x *log\e /

$$\frac{2}{x^{3} \log{\left(e^{1} \right)}}$$

Simplify

The graph