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 x/4
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Derivada de x^(2*x)
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Derivada de 6
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Derivada de x^(3*x)
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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 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
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
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) /
$$\left(\frac{1}{x \log{\left(2 x \right)} \log{\left(5 x \right)}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{x \log{\left(2 x \right)}^{2}}\right) \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}}$$
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)
$$\frac{\left(\frac{\left(\frac{1}{\log{\left(5 x \right)}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}}\right)^{2}}{\log{\left(2 x \right)}} - \frac{1}{\log{\left(5 x \right)}} - \frac{1}{\log{\left(5 x \right)}^{2}} + \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}} - \frac{2}{\log{\left(2 x \right)} \log{\left(5 x \right)}} + \frac{2 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}^{2}}\right) \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}}}{x^{2} \log{\left(2 x \right)}}$$
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)
$$\frac{\left(\frac{\left(\frac{1}{\log{\left(5 x \right)}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}}\right)^{3}}{\log{\left(2 x \right)}^{2}} - \frac{3 \left(\frac{1}{\log{\left(5 x \right)}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}}\right) \left(\frac{1}{\log{\left(5 x \right)}} + \frac{1}{\log{\left(5 x \right)}^{2}} - \frac{\log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}} + \frac{2}{\log{\left(2 x \right)} \log{\left(5 x \right)}} - \frac{2 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}^{2}}\right)}{\log{\left(2 x \right)}} + \frac{2}{\log{\left(5 x \right)}} + \frac{3}{\log{\left(5 x \right)}^{2}} + \frac{2}{\log{\left(5 x \right)}^{3}} - \frac{2 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}} + \frac{6}{\log{\left(2 x \right)} \log{\left(5 x \right)}} + \frac{3}{\log{\left(2 x \right)} \log{\left(5 x \right)}^{2}} - \frac{6 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}^{2}} + \frac{6}{\log{\left(2 x \right)}^{2} \log{\left(5 x \right)}} - \frac{6 \log{\left(\log{\left(5 x \right)} \right)}}{\log{\left(2 x \right)}^{3}}\right) \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}}}{x^{3} \log{\left(2 x \right)}}$$
Gráfico