Derivative of 1/ln(x)

The solution

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  1   
------
log(x)

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

1/log(x)

Detail solution

Let $u = \log{\left(x \right)}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x \right)}$ :
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
The result of the chain rule is:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   -1    
---------
     2   
x*log (x)

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

Simplify

The second derivative [src]

      2   
1 + ------
    log(x)
----------
 2    2   
x *log (x)

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

Simplify

The third derivative [src]

   /      3         3   \
-2*|1 + ------ + -------|
   |    log(x)      2   |
   \             log (x)/
-------------------------
         3    2          
        x *log (x)

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

Simplify

The graph

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Identical expressions

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Derivative of 1/ln(x)

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The solution