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 1/(x+3)
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Derivada de 4*y
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Derivada de (-1)/x-3*x
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Derivada de y=csc(3x²+1)
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Expresiones idénticas
- (x+e^x)^(uno /lnx)
- (x más e en el grado x) en el grado (1 dividir por lnx)
- (x más e en el grado x) en el grado (uno dividir por lnx)
- (x+ex)(1/lnx)
- x+ex1/lnx
- x+e^x^1/lnx
- (x+e^x)^(1 dividir por lnx)
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Expresiones semejantes
- (x-e^x)^(1/lnx)
Derivada de (x+e^x)^(1/lnx)
Solución
Ha introducido
[src]
1
------
log(x)
/ x\
\x + E /
$$\left(e^{x} + x\right)^{\frac{1}{\log{\left(x \right)}}}$$
(x + E^x)^(1/log(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(x) / x / x\\
/ x\ | 1 + E log\x + E /|
\x + E / *|--------------- - -----------|
|/ x\ 2 |
\\x + E /*log(x) x*log (x) /
$$\left(e^{x} + x\right)^{\frac{1}{\log{\left(x \right)}}} \left(\frac{e^{x} + 1}{\left(e^{x} + x\right) \log{\left(x \right)}} - \frac{\log{\left(e^{x} + x \right)}}{x \log{\left(x \right)}^{2}}\right)$$
Segunda derivada
[src]
/ 2 \
| / x / x\\ |
1 | |1 + e log\x + e /| |
------ | |------ - -----------| 2 |
log(x) | x | x x*log(x) | / x\ / x\ / x\ / x\ |
/ x\ | e \x + e / \1 + e / log\x + e / 2*log\x + e / 2*\1 + e / |
\x + e / *|------ + ----------------------- - --------- + ----------- + ------------- - -----------------|
| x log(x) 2 2 2 2 / x\ |
|x + e / x\ x *log(x) x *log (x) x*\x + e /*log(x)|
\ \x + e / /
---------------------------------------------------------------------------------------------------------------
log(x)
$$\frac{\left(x + e^{x}\right)^{\frac{1}{\log{\left(x \right)}}} \left(\frac{\left(\frac{e^{x} + 1}{x + e^{x}} - \frac{\log{\left(x + e^{x} \right)}}{x \log{\left(x \right)}}\right)^{2}}{\log{\left(x \right)}} + \frac{e^{x}}{x + e^{x}} - \frac{\left(e^{x} + 1\right)^{2}}{\left(x + e^{x}\right)^{2}} - \frac{2 \left(e^{x} + 1\right)}{x \left(x + e^{x}\right) \log{\left(x \right)}} + \frac{\log{\left(x + e^{x} \right)}}{x^{2} \log{\left(x \right)}} + \frac{2 \log{\left(x + e^{x} \right)}}{x^{2} \log{\left(x \right)}^{2}}\right)}{\log{\left(x \right)}}$$
Tercera derivada
[src]
/ / 2 \ \
| 3 / x / x\\ | x / x\ / x\ / x\ / x\ | |
| / x / x\\ |1 + e log\x + e /| | e \1 + e / log\x + e / 2*log\x + e / 2*\1 + e / | |
1 | |1 + e log\x + e /| 3*|------ - -----------|*|------ - --------- + ----------- + ------------- - -----------------| |
------ | |------ - -----------| 3 | x x*log(x) | | x 2 2 2 2 / x\ | 2 |
log(x) | x | x x*log(x) | / x\ / x\ / x\ / x\ x / x\ \x + e / |x + e / x\ x *log(x) x *log (x) x*\x + e /*log(x)| x / x\ / x\ / x\ |
/ x\ | e \x + e / 2*\1 + e / 6*log\x + e / 6*log\x + e / 3*\1 + e /*e 2*log\x + e / \ \x + e / / 3*e 3*\1 + e / 3*\1 + e / 6*\1 + e / |
\x + e / *|------ + ----------------------- + ----------- - ------------- - ------------- - ------------- - ------------- + ----------------------------------------------------------------------------------------------- - ----------------- + ------------------ + ------------------ + -------------------|
| x 2 3 3 3 3 2 2 3 log(x) / x\ 2 2 / x\ 2 / x\ 2 |
|x + e log (x) / x\ x *log (x) x *log (x) / x\ x *log(x) x*\x + e /*log(x) / x\ x *\x + e /*log(x) x *\x + e /*log (x)|
\ \x + e / \x + e / x*\x + e / *log(x) /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(x)
$$\frac{\left(x + e^{x}\right)^{\frac{1}{\log{\left(x \right)}}} \left(\frac{\left(\frac{e^{x} + 1}{x + e^{x}} - \frac{\log{\left(x + e^{x} \right)}}{x \log{\left(x \right)}}\right)^{3}}{\log{\left(x \right)}^{2}} + \frac{3 \left(\frac{e^{x} + 1}{x + e^{x}} - \frac{\log{\left(x + e^{x} \right)}}{x \log{\left(x \right)}}\right) \left(\frac{e^{x}}{x + e^{x}} - \frac{\left(e^{x} + 1\right)^{2}}{\left(x + e^{x}\right)^{2}} - \frac{2 \left(e^{x} + 1\right)}{x \left(x + e^{x}\right) \log{\left(x \right)}} + \frac{\log{\left(x + e^{x} \right)}}{x^{2} \log{\left(x \right)}} + \frac{2 \log{\left(x + e^{x} \right)}}{x^{2} \log{\left(x \right)}^{2}}\right)}{\log{\left(x \right)}} + \frac{e^{x}}{x + e^{x}} - \frac{3 \left(e^{x} + 1\right) e^{x}}{\left(x + e^{x}\right)^{2}} + \frac{2 \left(e^{x} + 1\right)^{3}}{\left(x + e^{x}\right)^{3}} - \frac{3 e^{x}}{x \left(x + e^{x}\right) \log{\left(x \right)}} + \frac{3 \left(e^{x} + 1\right)^{2}}{x \left(x + e^{x}\right)^{2} \log{\left(x \right)}} + \frac{3 \left(e^{x} + 1\right)}{x^{2} \left(x + e^{x}\right) \log{\left(x \right)}} + \frac{6 \left(e^{x} + 1\right)}{x^{2} \left(x + e^{x}\right) \log{\left(x \right)}^{2}} - \frac{2 \log{\left(x + e^{x} \right)}}{x^{3} \log{\left(x \right)}} - \frac{6 \log{\left(x + e^{x} \right)}}{x^{3} \log{\left(x \right)}^{2}} - \frac{6 \log{\left(x + e^{x} \right)}}{x^{3} \log{\left(x \right)}^{3}}\right)}{\log{\left(x \right)}}$$
Gráfico