Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^(4/3)
Derivative of -x/2
Derivative of x^2/log(x)
Derivative of ex^2
Identical expressions
(ln(ln(x)))^(ln(x))^(- one)
(ln(ln(x))) to the power of (ln(x)) to the power of ( minus 1)
(ln(ln(x))) to the power of (ln(x)) to the power of ( minus one)
(ln(ln(x)))(ln(x))(-1)
lnlnxlnx-1
lnlnx^lnx^-1
Similar expressions
(ln(ln(x)))^(ln(x))^(1)

The derivative of the function/ (ln(ln(x)))^(ln(x))^(-1)

Derivative of (ln(ln(x)))^(ln(x))^(-1)

The solution

You have entered [src]

               1   
             ------
             log(x)
(log(log(x)))

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

log(log(x))^(1/log(x))

Detail solution

Don't know the steps in finding this derivative.

But the derivative is

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

                    /                                                                      3                                                                                                                                                              /       1                        \ /     1                                    1            2*log(log(log(x)))           3         \\
               1    |                                    /       1                        \                                                                                                                                                             3*|- ----------- + log(log(log(x)))|*|----------- - log(log(log(x))) + ------------------- - ------------------ + ------------------||
             ------ |                                    |- ----------- + log(log(log(x)))|                                                                                                                                                               \  log(log(x))                   / |log(log(x))                                2                 log(x)         log(x)*log(log(x))||
             log(x) |                           2        \  log(log(x))                   /    6*log(log(log(x)))   6*log(log(log(x)))            2                      3                     6                     9                     11                                                \                                 log(x)*log (log(x))                                          /|
(log(log(x)))      *|-2*log(log(log(x))) + ----------- - ----------------------------------- - ------------------ - ------------------ + -------------------- + ------------------- + -------------------- + ------------------ + ------------------- + -------------------------------------------------------------------------------------------------------------------------------------|
                    |                      log(log(x))                    4                          log(x)                 2               2       3                     2              2       2           log(x)*log(log(x))      2                                                                                    2                                                                  |
                    \                                                  log (x)                                           log (x)         log (x)*log (log(x))   log(x)*log (log(x))   log (x)*log (log(x))                        log (x)*log(log(x))                                                                  log (x)                                                               /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                           3    2                                                                                                                                                                                             
                                                                                                                                                                                          x *log (x)

\frac{\left(- \frac{\left(\log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} - \frac{1}{\log{\left(\log{\left(x \right)} \right)}}\right)^{3}}{\log{\left(x \right)}^{4}} + \frac{3 \left(\log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} - \frac{1}{\log{\left(\log{\left(x \right)} \right)}}\right) \left(- \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} + \frac{1}{\log{\left(\log{\left(x \right)} \right)}} - \frac{2 \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}} + \frac{1}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{2}}\right)}{\log{\left(x \right)}^{2}} - 2 \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} + \frac{2}{\log{\left(\log{\left(x \right)} \right)}} - \frac{6 \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}}{\log{\left(x \right)}} + \frac{9}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}} + \frac{3}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{2}} - \frac{6 \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}}{\log{\left(x \right)}^{2}} + \frac{11}{\log{\left(x \right)}^{2} \log{\left(\log{\left(x \right)} \right)}} + \frac{6}{\log{\left(x \right)}^{2} \log{\left(\log{\left(x \right)} \right)}^{2}} + \frac{2}{\log{\left(x \right)}^{2} \log{\left(\log{\left(x \right)} \right)}^{3}}\right) \log{\left(\log{\left(x \right)} \right)}^{\frac{1}{\log{\left(x \right)}}}}{x^{3} \log{\left(x \right)}^{2}}

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of (ln(ln(x)))^(ln(x))^(-1)

The graph:

Piecewise:

The solution