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Derivada de:
Derivada de (x^5+1)
Derivada de 1/(x+1)^2
Derivada de x^-11
Derivada de 7
Expresiones idénticas
y=ln5x^(uno /ln2x)
y es igual a ln5x en el grado (1 dividir por ln2x)
y es igual a ln5x en el grado (uno dividir por ln2x)
y=ln5x(1/ln2x)
y=ln5x1/ln2x
y=ln5x^1/ln2x
y=ln5x^(1 dividir por ln2x)

Derivada de la función/ y=ln5/ y=ln5x^(1/ln2x)

Derivada de y=ln5x^(1/ln2x)

Solución

Ha introducido [src]

             1    
          --------
          log(2*x)
(log(5*x))

\log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}}

log(5*x)^(1/log(2*x))

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

             1                                          
          --------                                      
          log(2*x) /         1            log(log(5*x))\
(log(5*x))        *|------------------- - -------------|
                   |x*log(2*x)*log(5*x)         2      |
                   \                       x*log (2*x) /

\left(\frac{1}{x \log{\left(2 x \right)} \log{\left(5 x \right)}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{x \log{\left(2 x \right)}^{2}}\right) \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}}

Simplificar

Segunda derivada [src]

                   /                                                   2                                                      \
             1     |                         /   1       log(log(5*x))\                                                       |
          -------- |                         |-------- - -------------|                                                       |
          log(2*x) |     1           1       \log(5*x)      log(2*x)  /    log(log(5*x))           2           2*log(log(5*x))|
(log(5*x))        *|- -------- - --------- + --------------------------- + ------------- - ----------------- + ---------------|
                   |  log(5*x)      2                  log(2*x)               log(2*x)     log(2*x)*log(5*x)         2        |
                   \             log (5*x)                                                                        log (2*x)   /
-------------------------------------------------------------------------------------------------------------------------------
                                                           2                                                                   
                                                          x *log(2*x)

\frac{\left(\frac{\left(\frac{1}{\log{\left(5 x \right)}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}}\right)^{2}}{\log{\left(2 x \right)}} - \frac{1}{\log{\left(5 x \right)}} - \frac{1}{\log{\left(5 x \right)}^{2}} + \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}} - \frac{2}{\log{\left(2 x \right)} \log{\left(5 x \right)}} + \frac{2 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}^{2}}\right) \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}}}{x^{2} \log{\left(2 x \right)}}

Simplificar

Tercera derivada [src]

                   /                                                             3                                                                                                                         /   1       log(log(5*x))\ /   1           1       log(log(5*x))   2*log(log(5*x))           2        \\
             1     |                                   /   1       log(log(5*x))\                                                                                                                        3*|-------- - -------------|*|-------- + --------- - ------------- - --------------- + -----------------||
          -------- |                                   |-------- - -------------|                                                                                                                          \log(5*x)      log(2*x)  / |log(5*x)      2           log(2*x)           2           log(2*x)*log(5*x)||
          log(2*x) |   2           2           3       \log(5*x)      log(2*x)  /    6*log(log(5*x))   6*log(log(5*x))   2*log(log(5*x))           3                    6                   6                                         \           log (5*x)                      log (2*x)                       /|
(log(5*x))        *|-------- + --------- + --------- + --------------------------- - --------------- - --------------- - --------------- + ------------------ + ----------------- + ------------------ - ---------------------------------------------------------------------------------------------------------|
                   |log(5*x)      3           2                    2                       3                 2               log(2*x)                  2        log(2*x)*log(5*x)      2                                                                  log(2*x)                                                |
                   \           log (5*x)   log (5*x)            log (2*x)               log (2*x)         log (2*x)                        log(2*x)*log (5*x)                       log (2*x)*log(5*x)                                                                                                            /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                     3                                                                                                                                                             
                                                                                                                                                    x *log(2*x)

\frac{\left(\frac{\left(\frac{1}{\log{\left(5 x \right)}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}}\right)^{3}}{\log{\left(2 x \right)}^{2}} - \frac{3 \left(\frac{1}{\log{\left(5 x \right)}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}}\right) \left(\frac{1}{\log{\left(5 x \right)}} + \frac{1}{\log{\left(5 x \right)}^{2}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}} + \frac{2}{\log{\left(2 x \right)} \log{\left(5 x \right)}} - \frac{2 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}^{2}}\right)}{\log{\left(2 x \right)}} + \frac{2}{\log{\left(5 x \right)}} + \frac{3}{\log{\left(5 x \right)}^{2}} + \frac{2}{\log{\left(5 x \right)}^{3}} - \frac{2 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}} + \frac{6}{\log{\left(2 x \right)} \log{\left(5 x \right)}} + \frac{3}{\log{\left(2 x \right)} \log{\left(5 x \right)}^{2}} - \frac{6 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}^{2}} + \frac{6}{\log{\left(2 x \right)}^{2} \log{\left(5 x \right)}} - \frac{6 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}^{3}}\right) \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}}}{x^{3} \log{\left(2 x \right)}}

Simplificar

Gráfico

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Expresiones idénticas

Derivada de y=ln5x^(1/ln2x)

Gráfico:

Definida a trozos:

Solución