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Derivada de:
Derivada de b
Derivada de (3x+6)^2
Derivada de 2*y-4
Derivada de 1/rootx
Expresiones idénticas
x^((ln(uno 6x)^1/ dos))
x en el grado ((ln(16x) en el grado 1 dividir por 2))
x en el grado ((ln(uno 6x) en el grado 1 dividir por dos))
x((ln(16x)1/2))
xln16x1/2
x^ln16x^1/2
x^((ln(16x)^1 dividir por 2))

Derivada de la función/ x^((ln(16x)^1/2))

Derivada de x^((ln(16x)^1/2))

Solución

Ha introducido [src]

   ___________
 \/ log(16*x) 
x

x^{\sqrt{\log{\left(16 x \right)}}}

x^(sqrt(log(16*x)))

Solución detallada

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

Perola derivada

$\left(\log{\left(\sqrt{\log{\left(16 x \right)}} \right)} + 1\right) \log{\left(16 x \right)}^{\frac{\sqrt{\log{\left(16 x \right)}}}{2}}$

Respuesta:

$\left(\log{\left(\sqrt{\log{\left(16 x \right)}} \right)} + 1\right) \log{\left(16 x \right)}^{\frac{\sqrt{\log{\left(16 x \right)}}}{2}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

   ___________ /  ___________                    \
 \/ log(16*x)  |\/ log(16*x)          log(x)     |
x             *|------------- + -----------------|
               |      x               ___________|
               \                2*x*\/ log(16*x) /

x^{\sqrt{\log{\left(16 x \right)}}} \left(\frac{\log{\left(x \right)}}{2 x \sqrt{\log{\left(16 x \right)}}} + \frac{\sqrt{\log{\left(16 x \right)}}}{x}\right)

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Segunda derivada [src]

               /                                                                 2                                   \
               |                                /    ___________       log(x)   \                                    |
               |                                |2*\/ log(16*x)  + -------------|                                    |
   ___________ |                                |                    ___________|                                    |
 \/ log(16*x)  |      1           ___________   \                  \/ log(16*x) /         log(x)           log(x)    |
x             *|------------- - \/ log(16*x)  + ---------------------------------- - --------------- - --------------|
               |  ___________                                   4                        ___________        3/2      |
               \\/ log(16*x)                                                         2*\/ log(16*x)    4*log   (16*x)/
----------------------------------------------------------------------------------------------------------------------
                                                           2                                                          
                                                          x

\frac{x^{\sqrt{\log{\left(16 x \right)}}} \left(\frac{\left(\frac{\log{\left(x \right)}}{\sqrt{\log{\left(16 x \right)}}} + 2 \sqrt{\log{\left(16 x \right)}}\right)^{2}}{4} - \frac{\log{\left(x \right)}}{2 \sqrt{\log{\left(16 x \right)}}} - \frac{\log{\left(x \right)}}{4 \log{\left(16 x \right)}^{\frac{3}{2}}} - \sqrt{\log{\left(16 x \right)}} + \frac{1}{\sqrt{\log{\left(16 x \right)}}}\right)}{x^{2}}

Simplificar

Tercera derivada [src]

               /                                                                                      3                                                                                                                                                           \
               |                                                     /    ___________       log(x)   \                      /    ___________       log(x)   \ /        4             ___________      log(x)         2*log(x)  \                                  |
               |                                                     |2*\/ log(16*x)  + -------------|                    3*|2*\/ log(16*x)  + -------------|*|- ------------- + 4*\/ log(16*x)  + ------------ + -------------|                                  |
   ___________ |                                                     |                    ___________|                      |                    ___________| |    ___________                        3/2           ___________|                                  |
 \/ log(16*x)  |        3             ___________         3          \                  \/ log(16*x) /        log(x)        \                  \/ log(16*x) / \  \/ log(16*x)                      log   (16*x)   \/ log(16*x) /      3*log(x)         3*log(x)   |
x             *|- ------------- + 2*\/ log(16*x)  - -------------- + ---------------------------------- + ------------- - ------------------------------------------------------------------------------------------------------ + -------------- + --------------|
               |    ___________                          3/2                         8                      ___________                                                     8                                                           3/2              5/2      |
               \  \/ log(16*x)                      4*log   (16*x)                                        \/ log(16*x)                                                                                                             4*log   (16*x)   8*log   (16*x)/
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                  3                                                                                                                                
                                                                                                                                 x

\frac{x^{\sqrt{\log{\left(16 x \right)}}} \left(\frac{\left(\frac{\log{\left(x \right)}}{\sqrt{\log{\left(16 x \right)}}} + 2 \sqrt{\log{\left(16 x \right)}}\right)^{3}}{8} - \frac{3 \left(\frac{\log{\left(x \right)}}{\sqrt{\log{\left(16 x \right)}}} + 2 \sqrt{\log{\left(16 x \right)}}\right) \left(\frac{2 \log{\left(x \right)}}{\sqrt{\log{\left(16 x \right)}}} + \frac{\log{\left(x \right)}}{\log{\left(16 x \right)}^{\frac{3}{2}}} + 4 \sqrt{\log{\left(16 x \right)}} - \frac{4}{\sqrt{\log{\left(16 x \right)}}}\right)}{8} + \frac{\log{\left(x \right)}}{\sqrt{\log{\left(16 x \right)}}} + \frac{3 \log{\left(x \right)}}{4 \log{\left(16 x \right)}^{\frac{3}{2}}} + \frac{3 \log{\left(x \right)}}{8 \log{\left(16 x \right)}^{\frac{5}{2}}} + 2 \sqrt{\log{\left(16 x \right)}} - \frac{3}{\sqrt{\log{\left(16 x \right)}}} - \frac{3}{4 \log{\left(16 x \right)}^{\frac{3}{2}}}\right)}{x^{3}}

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Gráfico

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Expresiones idénticas

Derivada de x^((ln(16x)^1/2))

Gráfico:

Definida a trozos:

Solución