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(сtg(x))^(uno /(ln(x)))
(сtg(x)) en el grado (1 dividir por (ln(x)))
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(сtg(x))(1/(ln(x)))
сtgx1/lnx
сtgx^1/lnx
(сtg(x))^(1 dividir por (ln(x)))
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ln
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ln^2(2x-1)
ln(x)/sqrt(x)
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ln√x

Derivada de la función/ tg(x)/ ln(x)/ (сtg(x))^(1/(ln(x)))

Derivada de (сtg(x))^(1/(ln(x)))

Solución

Ha introducido [src]

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

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

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

Solución detallada

No logro encontrar los pasos en la búsqueda de esta derivada.

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

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Expresiones idénticas

Expresiones con funciones

Derivada de (сtg(x))^(1/(ln(x)))

Gráfico:

Definida a trozos:

Solución