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 -2x
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Derivada de e^-1
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Derivada de y
- Derivada de x^e^x
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Expresiones idénticas
- (x/tgx)^e^cosx
- (x dividir por tgx) en el grado e en el grado coseno de x
- (x/tgx)ecosx
- x/tgxecosx
- x/tgx^e^cosx
- (x dividir por tgx)^e^cosx
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Expresiones con funciones
- tgx
- tgx-ctgx
- cosx
- cosx/lnx
Derivada de (x/tgx)^e^cosx
Solución
Ha introducido
[src]
/ cos(x)\
\E /
/ x \
|------|
\tan(x)/
$$\left(\frac{x}{\tan{\left(x \right)}}\right)^{e^{\cos{\left(x \right)}}}$$
(x/tan(x))^(E^cos(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]
/ / / 2 \\ \
| | 1 x*\-1 - tan (x)/| cos(x) |
/ cos(x)\ | |------ + ----------------|*e *tan(x)|
\E / | |tan(x) 2 | |
/ x \ | cos(x) / x \ \ tan (x) / |
|------| *|- e *log|------|*sin(x) + ------------------------------------------|
\tan(x)/ \ \tan(x)/ x /
$$\left(\frac{x}{\tan{\left(x \right)}}\right)^{e^{\cos{\left(x \right)}}} \left(- e^{\cos{\left(x \right)}} \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\left(\frac{x \left(- \tan^{2}{\left(x \right)} - 1\right)}{\tan^{2}{\left(x \right)}} + \frac{1}{\tan{\left(x \right)}}\right) e^{\cos{\left(x \right)}} \tan{\left(x \right)}}{x}\right)$$
Segunda derivada
[src]
/ 2 / / 2 \\ \
| / 2 \ / / 2 \ \ / 2 \ | 1 x*\1 + tan (x)/| / / 2 \\ / / 2 \\|
/ cos(x)\ | x*\1 + tan (x)/ | x*\1 + tan (x)/ | 2*\1 + tan (x)/*|x + ------ - ---------------| | x*\1 + tan (x)/| / 2 \ | x*\1 + tan (x)/||
\e / |-1 + --------------- |-1 + --------------- | | tan(x) 2 | 2*|-1 + ---------------|*sin(x) \1 + tan (x)/*|-1 + ---------------||
/ x \ | tan(x) | tan(x) / x \ | cos(x) 2 / x \ / x \ \ tan (x) / \ tan(x) / \ tan(x) /| cos(x)
|------| *|-------------------- + |-------------------- + log|------|*sin(x)| *e + sin (x)*log|------| - cos(x)*log|------| - ---------------------------------------------- + ------------------------------- - ------------------------------------|*e
\tan(x)/ | 2 \ x \tan(x)/ / \tan(x)/ \tan(x)/ x x x*tan(x) |
\ x /
$$\left(\frac{x}{\tan{\left(x \right)}}\right)^{e^{\cos{\left(x \right)}}} \left(\left(\log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1}{x}\right)^{2} e^{\cos{\left(x \right)}} + \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin^{2}{\left(x \right)} - \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \cos{\left(x \right)} - \frac{\left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x \tan{\left(x \right)}} + \frac{2 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \sin{\left(x \right)}}{x} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + x + \frac{1}{\tan{\left(x \right)}}\right)}{x} + \frac{\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1}{x^{2}}\right) e^{\cos{\left(x \right)}}$$
Tercera derivada
[src]
/ / 2\ \
| 3 / / 2 \\ / / / 2 \\ \ / / 2 \\ | / 2 \ / 2 \ / 2 \ | 2 / / 2 \\ |
|/ / 2 \ \ / / 2 \\ / 2 \ | 1 x*\1 + tan (x)/| / / 2 \\ / / 2 \\ / / 2 \\ / / 2 \\ / / 2 \ \ | / 2 \ / 2 \ | 1 x*\1 + tan (x)/| / / 2 \\ / / 2 \\| / 2 \ | 1 x*\1 + tan (x)/| / / 2 \\ / 2 \ | 3 3*\1 + tan (x)/ 5*x*\1 + tan (x)/ 3*x*\1 + tan (x)/ | / 2 \ | 1 x*\1 + tan (x)/| / / 2 \\ |
/ cos(x)\ || x*\1 + tan (x)/ | | x*\1 + tan (x)/| 4*\1 + tan (x)/*|x + ------ - ---------------| | x*\1 + tan (x)/| / 2 \ | x*\1 + tan (x)/| 2 | x*\1 + tan (x)/| | x*\1 + tan (x)/| | x*\1 + tan (x)/ | | x*\1 + tan (x)/ 2*\1 + tan (x)/*|x + ------ - ---------------| | x*\1 + tan (x)/| / 2 \ | x*\1 + tan (x)/|| 6*\1 + tan (x)/*|x + ------ - ---------------|*sin(x) / 2 \ | x*\1 + tan (x)/| 2*\1 + tan (x)/*|2*x + ------ - --------------- - ----------------- + ------------------|*tan(x) 4*\1 + tan (x)/ *|x + ------ - ---------------| / 2 \ | x*\1 + tan (x)/| |
\e / ||-1 + --------------- | 2*|-1 + ---------------| | tan(x) 2 | 3*|-1 + ---------------|*cos(x) 2*\1 + tan (x)/*|-1 + ---------------| 3*sin (x)*|-1 + ---------------| 3*|-1 + ---------------|*sin(x) |-1 + --------------- | |-1 + --------------- | tan(x) 2 | 2*|-1 + ---------------|*sin(x) \1 + tan (x)/*|-1 + ---------------|| | tan(x) 2 | 2*\1 + tan (x)/*|-1 + ---------------| | tan(x) 3 2 4 | | tan(x) 2 | 3*\1 + tan (x)/*|-1 + ---------------|*sin(x)|
/ x \ || tan(x) / x \ | 2*cos(x) 3 / x \ / x \ \ tan(x) / \ tan (x) / \ tan(x) / / x \ \ tan(x) / \ tan(x) / \ tan(x) / | tan(x) / x \ | | tan(x) 2 / x \ / x \ \ tan (x) / \ tan(x) / \ tan(x) /| cos(x) \ tan (x) / \ tan(x) / \ tan (x) tan (x) tan (x) / \ tan (x) / \ tan(x) / | cos(x)
-|------| *||-------------------- + log|------|*sin(x)| *e + sin (x)*log|------| - log|------|*sin(x) + ------------------------ - ---------------------------------------------- - ------------------------------- - 3*cos(x)*log|------|*sin(x) + -------------------------------------- + -------------------------------- + ------------------------------- + 3*|-------------------- + log|------|*sin(x)|*|-------------------- + sin (x)*log|------| - cos(x)*log|------| - ---------------------------------------------- + ------------------------------- - ------------------------------------|*e - ----------------------------------------------------- - -------------------------------------- + ------------------------------------------------------------------------------------------------ + ----------------------------------------------- - ---------------------------------------------|*e
\tan(x)/ |\ x \tan(x)/ / \tan(x)/ \tan(x)/ 3 2 x \tan(x)/ x x 2 \ x \tan(x)/ / | 2 \tan(x)/ \tan(x)/ x x x*tan(x) | x 2 x x*tan(x) x*tan(x) |
\ x x x \ x / x *tan(x) /
$$- \left(\frac{x}{\tan{\left(x \right)}}\right)^{e^{\cos{\left(x \right)}}} \left(\left(\log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1}{x}\right)^{3} e^{2 \cos{\left(x \right)}} + 3 \left(\log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1}{x}\right) \left(\log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin^{2}{\left(x \right)} - \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \cos{\left(x \right)} - \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)}{x \tan{\left(x \right)}} + \frac{2 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \sin{\left(x \right)}}{x} - \frac{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)}{x} + \frac{\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1}{x^{2}}\right) e^{\cos{\left(x \right)}} + \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin^{3}{\left(x \right)} - 3 \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} \cos{\left(x \right)} - \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} - \frac{3 \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) \sin{\left(x \right)}}{x \tan{\left(x \right)}} + \frac{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)}{x} + \frac{3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \sin^{2}{\left(x \right)}}{x} - \frac{3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x} + \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)}{x \tan{\left(x \right)}} - \frac{6 \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) \sin{\left(x \right)}}{x} + \frac{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)}}{x} - \frac{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)}{x^{2} \tan{\left(x \right)}} + \frac{3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \sin{\left(x \right)}}{x^{2}} - \frac{4 \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^{2}} + \frac{2 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right)}{x^{3}}\right) e^{\cos{\left(x \right)}}$$
Gráfico