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:
-
Derivada de (x⁴-10)
- Derivada de x^2/a^2
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Derivada de x^(-2/7)
- Derivada de √x(2x-4)
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Expresiones idénticas
- (x/tan(x))^(uno /(x^ dos))
- (x dividir por tangente de (x)) en el grado (1 dividir por (x al cuadrado ))
- (x dividir por tangente de (x)) en el grado (uno dividir por (x en el grado dos))
- (x/tan(x))(1/(x2))
- x/tanx1/x2
- (x/tan(x))^(1/(x²))
- (x/tan(x)) en el grado (1/(x en el grado 2))
- x/tanx^1/x^2
- (x dividir por tan(x))^(1 dividir por (x^2))
Derivada de (x/tan(x))^(1/(x^2))
Solución
Ha introducido
[src]
1
--
2
x
/ x \
|------|
\tan(x)/
$$\left(\frac{x}{\tan{\left(x \right)}}\right)^{\frac{1}{x^{2}}}$$
(x/tan(x))^(1/(x^2))
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]
1 / / / 2 \\ \
-- | | 1 x*\-1 - tan (x)/| |
2 | / x \ |------ + ----------------|*tan(x)|
x | 2*log|------| |tan(x) 2 | |
/ x \ | \tan(x)/ \ tan (x) / |
|------| *|- ------------- + ----------------------------------|
\tan(x)/ | 3 3 |
\ x x /
$$\left(\frac{x}{\tan{\left(x \right)}}\right)^{\frac{1}{x^{2}}} \left(\frac{\left(\frac{x \left(- \tan^{2}{\left(x \right)} - 1\right)}{\tan^{2}{\left(x \right)}} + \frac{1}{\tan{\left(x \right)}}\right) \tan{\left(x \right)}}{x^{3}} - \frac{2 \log{\left(\frac{x}{\tan{\left(x \right)}} \right)}}{x^{3}}\right)$$
Segunda derivada
[src]
1 / 2 \
-- |/ / 2 \\ / / 2 \\ / / 2 \\|
2 || / x \ x*\1 + tan (x)/| | x*\1 + tan (x)/| / x \ / 2 \ | x*\1 + tan (x)/||
x ||-1 + 2*log|------| + ---------------| / / 2 \\ 5*|-1 + ---------------| 6*log|------| \1 + tan (x)/*|-1 + ---------------||
/ x \ |\ \tan(x)/ tan(x) / / 2 \ | 1 x*\1 + tan (x)/| \ tan(x) / \tan(x)/ \ tan(x) /|
|------| *|--------------------------------------- - 2*\1 + tan (x)/*|x + ------ - ---------------| + ------------------------ + ------------- - ------------------------------------|
\tan(x)/ | 3 | tan(x) 2 | x x tan(x) |
\ x \ tan (x) / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
x
$$\frac{\left(\frac{x}{\tan{\left(x \right)}}\right)^{\frac{1}{x^{2}}} \left(- \frac{\left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + x + \frac{1}{\tan{\left(x \right)}}\right) + \frac{5 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right)}{x} + \frac{6 \log{\left(\frac{x}{\tan{\left(x \right)}} \right)}}{x} + \frac{\left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + 2 \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} - 1\right)^{2}}{x^{3}}\right)}{x^{3}}$$
Tercera derivada
[src]
/ / / / 2 \\ / / 2 \\\ \
| | / x \ | x*\1 + tan (x)/| / 2 \ | x*\1 + tan (x)/|| |
1 | 3 2 / / 2 \\ / / 2 \\ | 6*log|------| 5*|-1 + ---------------| / / 2 \\ \1 + tan (x)/*|-1 + ---------------|| / / 2 \\ |
-- | / / 2 \\ / / 2 \\ / 2 \ | 1 x*\1 + tan (x)/| | / x \ x*\1 + tan (x)/| | \tan(x)/ \ tan(x) / / 2 \ | 1 x*\1 + tan (x)/| \ tan(x) /| / 2 \ | 1 x*\1 + tan (x)/| / / 2 \\|
2 | | / x \ x*\1 + tan (x)/| | x*\1 + tan (x)/| / x \ 4*\1 + tan (x)/ *|x + ------ - ---------------| / 2\ 3*|-1 + 2*log|------| + ---------------|*|- ------------- - ------------------------ + 2*\1 + tan (x)/*|x + ------ - ---------------| + ------------------------------------| 16*\1 + tan (x)/*|x + ------ - ---------------| / 2 \ | x*\1 + tan (x)/||
x | |-1 + 2*log|------| + ---------------| 26*|-1 + ---------------| 24*log|------| / / 2 \\ | tan(x) 2 | | / 2 \ / 2 \ / 2 \ | \ \tan(x)/ tan(x) / | x x | tan(x) 2 | tan(x) | | tan(x) 2 | 8*\1 + tan (x)/*|-1 + ---------------||
/ x \ | \ \tan(x)/ tan(x) / \ tan(x) / \tan(x)/ / 2 \ | x*\1 + tan (x)/| \ tan (x) / / 2 \ | 3 3*\1 + tan (x)/ 5*x*\1 + tan (x)/ 3*x*\1 + tan (x)/ | \ \ tan (x) / / \ tan (x) / \ tan(x) /|
|------| *|- --------------------------------------- - ------------------------- - -------------- - 2*\1 + tan (x)/*|-1 + ---------------| - ----------------------------------------------- - 2*\1 + tan (x)/*|2*x + ------ - --------------- - ----------------- + ------------------|*tan(x) + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------- + --------------------------------------|
\tan(x)/ | 6 2 2 \ tan(x) / tan(x) | tan(x) 3 2 4 | 3 x x*tan(x) |
\ x x x \ tan (x) tan (x) tan (x) / x /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
x
$$\frac{\left(\frac{x}{\tan{\left(x \right)}}\right)^{\frac{1}{x^{2}}} \left(- 2 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + x + \frac{1}{\tan{\left(x \right)}}\right)}{\tan{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{4}{\left(x \right)}} - \frac{5 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 x - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{3}{\left(x \right)}} + \frac{3}{\tan{\left(x \right)}}\right) \tan{\left(x \right)} + \frac{8 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x \tan{\left(x \right)}} + \frac{16 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + x + \frac{1}{\tan{\left(x \right)}}\right)}{x} - \frac{26 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right)}{x^{2}} - \frac{24 \log{\left(\frac{x}{\tan{\left(x \right)}} \right)}}{x^{2}} + \frac{3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + 2 \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} - 1\right) \left(\frac{\left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + x + \frac{1}{\tan{\left(x \right)}}\right) - \frac{5 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right)}{x} - \frac{6 \log{\left(\frac{x}{\tan{\left(x \right)}} \right)}}{x}\right)}{x^{3}} - \frac{\left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + 2 \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} - 1\right)^{3}}{x^{6}}\right)}{x^{3}}$$
Gráfico