Mister Exam

Derivative of ln(lnx)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(log(x))
$$\log{\left(\log{\left(x \right)} \right)}$$
log(log(x))
Detail solution
  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    1. The derivative of is .

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
   1    
--------
x*log(x)
$$\frac{1}{x \log{\left(x \right)}}$$
The second derivative [src]
 /      1   \ 
-|1 + ------| 
 \    log(x)/ 
--------------
   2          
  x *log(x)   
$$- \frac{1 + \frac{1}{\log{\left(x \right)}}}{x^{2} \log{\left(x \right)}}$$
The third derivative [src]
       2        3   
2 + ------- + ------
       2      log(x)
    log (x)         
--------------------
      3             
     x *log(x)      
$$\frac{2 + \frac{3}{\log{\left(x \right)}} + \frac{2}{\log{\left(x \right)}^{2}}}{x^{3} \log{\left(x \right)}}$$
The graph
Derivative of ln(lnx)