Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de (π-2x)³
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Derivada de y=e×
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Derivada de y*log(5*y-1)
- Derivada de y=ln((sqrt(x))+(sqrt(x+a)))
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Expresiones idénticas
- x^(log(x,exp))
- x en el grado ( logaritmo de (x, exponente de ))
- x(log(x,exp))
- xlogx,exp
- x^logx,exp
Derivada de x^(log(x,exp))
Solución
Ha introducido
[src]
log(x)
-------
/ x\
log\e /
x
$$x^{\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}}}$$
x^(log(x)/log(exp(x)))
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
log(x)
-------
/ x\
log\e / // 1 log(x) \ log(x) \
x *||--------- - --------|*log(x) + ---------|
|| / x\ 2/ x\| / x\|
\\x*log\e / log \e // x*log\e //
$$x^{\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}}} \left(\left(- \frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}^{2}} + \frac{1}{x \log{\left(e^{x} \right)}}\right) \log{\left(x \right)} + \frac{\log{\left(x \right)}}{x \log{\left(e^{x} \right)}}\right)$$
Segunda derivada
[src]
/ 2 \
log(x) | 1 log(x) / 2 log(x)\ 2 |
------- | - - + ------- |- - + -------| *log (x) |
/ x\ | x / x\ | x / x\| |
log\e / |1 log\e / log(x) /1 2*log(x) 2 \ \ log\e // log(x) |
x *|-- - ------------- - ------ - |-- - -------- + ---------|*log(x) + ------------------------ - ---------|
| 2 x 2 | 2 2/ x\ / x\| / x\ / x\|
\x x \x log \e / x*log\e // log\e / x*log\e //
------------------------------------------------------------------------------------------------------------------
/ x\
log\e /
$$\frac{x^{\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}}} \left(\frac{\left(\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}} - \frac{2}{x}\right)^{2} \log{\left(x \right)}^{2}}{\log{\left(e^{x} \right)}} - \left(- \frac{2 \log{\left(x \right)}}{\log{\left(e^{x} \right)}^{2}} + \frac{2}{x \log{\left(e^{x} \right)}} + \frac{1}{x^{2}}\right) \log{\left(x \right)} - \frac{\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}} - \frac{1}{x}}{x} - \frac{\log{\left(x \right)}}{x \log{\left(e^{x} \right)}} - \frac{\log{\left(x \right)}}{x^{2}} + \frac{1}{x^{2}}\right)}{\log{\left(e^{x} \right)}}$$
Tercera derivada
[src]
/ / 1 log(x) \ \
| | - - + ------- | |
| 3 | x / x\ | |
log(x) | 1 log(x) /1 2*log(x) 2 \ / 2 log(x)\ 3 / 2 log(x)\ | 1 log\e / log(x) /1 2*log(x) 2 \ log(x) | |
------- | - - + ------- 2*|-- - -------- + ---------| |- - + -------| *log (x) 3*|- - + -------|*|- -- + ------------- + ------ + |-- - -------- + ---------|*log(x) + ---------|*log(x)|
/ x\ | x / x\ | 2 2/ x\ / x\| | x / x\| | x / x\| | 2 x 2 | 2 2/ x\ / x\| / x\| |
log\e / | 3 log\e / /2 6*log(x) 3 6 \ \x log \e / x*log\e // 2 2*log(x) \ log\e // 2*log(x) 2*log(x) \ log\e // \ x x \x log \e / x*log\e // x*log\e // |
x *|- -- + ------------- + |-- - -------- + ---------- + ----------|*log(x) - ----------------------------- - ---------- + -------- - ------------------------ + ---------- + ---------- + ---------------------------------------------------------------------------------------------------------|
| 3 2 | 3 3/ x\ 2 / x\ 2/ x\| x 2 / x\ 3 2/ x\ 2/ x\ 2 / x\ / x\ |
\ x x \x log \e / x *log\e / x*log \e // x *log\e / x log \e / x*log \e / x *log\e / log\e / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ x\
log\e /
$$\frac{x^{\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}}} \left(- \frac{\left(\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}} - \frac{2}{x}\right)^{3} \log{\left(x \right)}^{3}}{\log{\left(e^{x} \right)}^{2}} + \frac{3 \left(\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}} - \frac{2}{x}\right) \left(\left(- \frac{2 \log{\left(x \right)}}{\log{\left(e^{x} \right)}^{2}} + \frac{2}{x \log{\left(e^{x} \right)}} + \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}} - \frac{1}{x}}{x} + \frac{\log{\left(x \right)}}{x \log{\left(e^{x} \right)}} + \frac{\log{\left(x \right)}}{x^{2}} - \frac{1}{x^{2}}\right) \log{\left(x \right)}}{\log{\left(e^{x} \right)}} + \left(- \frac{6 \log{\left(x \right)}}{\log{\left(e^{x} \right)}^{3}} + \frac{6}{x \log{\left(e^{x} \right)}^{2}} + \frac{3}{x^{2} \log{\left(e^{x} \right)}} + \frac{2}{x^{3}}\right) \log{\left(x \right)} - \frac{2 \left(- \frac{2 \log{\left(x \right)}}{\log{\left(e^{x} \right)}^{2}} + \frac{2}{x \log{\left(e^{x} \right)}} + \frac{1}{x^{2}}\right)}{x} + \frac{2 \log{\left(x \right)}}{x \log{\left(e^{x} \right)}^{2}} + \frac{\frac{\log{\left(x \right)}}{\log{\left(e^{x} \right)}} - \frac{1}{x}}{x^{2}} + \frac{2 \log{\left(x \right)}}{x^{2} \log{\left(e^{x} \right)}} - \frac{2}{x^{2} \log{\left(e^{x} \right)}} + \frac{2 \log{\left(x \right)}}{x^{3}} - \frac{3}{x^{3}}\right)}{\log{\left(e^{x} \right)}}$$
Gráfico