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/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- x^((sinx)^cosx)
- x en el grado (( seno de x) en el grado coseno de x)
- x((sinx)cosx)
- xsinxcosx
- x^sinx^cosx
Derivada de x^((sinx)^cosx)
Solución
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
cos(x) / cos(x) / 2 \ \
sin (x) |sin (x) cos(x) |cos (x) | |
x *|------------ + sin (x)*|------- - log(sin(x))*sin(x)|*log(x)|
\ x \ sin(x) / /
$$x^{\sin^{\cos{\left(x \right)}}{\left(x \right)}} \left(\left(- \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} \sin^{\cos{\left(x \right)}}{\left(x \right)} + \frac{\sin^{\cos{\left(x \right)}}{\left(x \right)}}{x}\right)$$
Segunda derivada
[src]
/ / 2 \ \
| 2 2 | cos (x)| |
cos(x) | / / 2 \ \ / 2 \ 2*|log(sin(x))*sin(x) - -------| / 2 \ |
sin (x) cos(x) | 1 | 1 | cos (x)| | cos(x) | cos (x)| \ sin(x)/ | cos (x) | |
x *sin (x)*|- -- + |- - + |log(sin(x))*sin(x) - -------|*log(x)| *sin (x) + |log(sin(x))*sin(x) - -------| *log(x) - -------------------------------- - |3 + ------- + log(sin(x))|*cos(x)*log(x)|
| 2 \ x \ sin(x)/ / \ sin(x)/ x | 2 | |
\ x \ sin (x) / /
$$x^{\sin^{\cos{\left(x \right)}}{\left(x \right)}} \left(\left(\left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} - \frac{1}{x}\right)^{2} \sin^{\cos{\left(x \right)}}{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \log{\left(x \right)} - \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \log{\left(x \right)} \cos{\left(x \right)} - \frac{2 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)}{x} - \frac{1}{x^{2}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 2 / 2 \ \
| / 2 \ / 2 \ | cos (x) | / / 2 \ \ |
| 3 3 | cos (x)| | cos (x)| 3*|3 + ------- + log(sin(x))|*cos(x) | 2 | cos (x)| | |
cos(x) | / 2 4 \ / / 2 \ \ / 2 \ 3*|log(sin(x))*sin(x) - -------| 3*|log(sin(x))*sin(x) - -------| | 2 | / / 2 \ \ | / 2 \ 2*|log(sin(x))*sin(x) - -------| / 2 \ | / 2 \ / 2 \ |
sin (x) cos(x) |2 | 2*cos (x) 2*cos (x)| | 1 | cos (x)| | 2*cos(x) | cos (x)| \ sin(x)/ \ sin(x)/ \ sin (x) / cos(x) | 1 | cos (x)| | |1 | cos (x)| \ sin(x)/ | cos (x) | | | cos (x)| | cos (x) | |
x *sin (x)*|-- + |3*sin(x) + log(sin(x))*sin(x) + --------- + ---------|*log(x) - |- - + |log(sin(x))*sin(x) - -------|*log(x)| *sin (x) - |log(sin(x))*sin(x) - -------| *log(x) + --------------------------------- + -------------------------------- - ------------------------------------ + 3*sin (x)*|- - + |log(sin(x))*sin(x) - -------|*log(x)|*|-- - |log(sin(x))*sin(x) - -------| *log(x) + -------------------------------- + |3 + ------- + log(sin(x))|*cos(x)*log(x)| + 3*|log(sin(x))*sin(x) - -------|*|3 + ------- + log(sin(x))|*cos(x)*log(x)|
| 3 | sin(x) 3 | \ x \ sin(x)/ / \ sin(x)/ x 2 x \ x \ sin(x)/ / | 2 \ sin(x)/ x | 2 | | \ sin(x)/ | 2 | |
\x \ sin (x) / x \x \ sin (x) / / \ sin (x) / /
$$x^{\sin^{\cos{\left(x \right)}}{\left(x \right)}} \left(- \left(\left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} - \frac{1}{x}\right)^{3} \sin^{2 \cos{\left(x \right)}}{\left(x \right)} + 3 \left(\left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} - \frac{1}{x}\right) \left(- \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \log{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)}{x} + \frac{1}{x^{2}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)} - \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \log{\left(x \right)} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \log{\left(x \right)} \cos{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + 3 \sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{4}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) \log{\left(x \right)} + \frac{3 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2}}{x} - \frac{3 \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{x} + \frac{3 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)}{x^{2}} + \frac{2}{x^{3}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}$$
Gráfico