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 (2x-7)^8
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Derivada de (-1)/x-3*x
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Expresiones idénticas
- x^exp(x)^cos(x)
- x en el grado exponente de (x) en el grado coseno de (x)
- xexp(x)cos(x)
- xexpxcosx
- x^expx^cosx
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Expresiones semejantes
- x^exp(x)^cosx
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Expresiones con funciones
- Coseno cos
- cos(4*x+6)^(2)
- cos(log(x))+x^2*tan(x)
- cos(-6x+7)
- cos(3)+x^2
- cos(3*x)/3
Derivada de x^exp(x)^cos(x)
Solución
Ha introducido
[src]
/ cos(x)\ |/ x\ | \\e / / x
$$x^{\left(e^{x}\right)^{\cos{\left(x \right)}}}$$
x^(exp(x)^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]
/ cos(x)\
|/ x\ | / x*cos(x) \
\\e / / |e x*cos(x) |
x *|--------- + (-x*sin(x) + cos(x))*e *log(x)|
\ x /
$$x^{\left(e^{x}\right)^{\cos{\left(x \right)}}} \left(\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) e^{x \cos{\left(x \right)}} \log{\left(x \right)} + \frac{e^{x \cos{\left(x \right)}}}{x}\right)$$
Segunda derivada
[src]
/ x*cos(x)\ / 2 \
\e / | 1 / 1 \ x*cos(x) 2 2*(-cos(x) + x*sin(x))| x*cos(x)
x *|- -- + |- - + (-cos(x) + x*sin(x))*log(x)| *e + (-cos(x) + x*sin(x)) *log(x) - (2*sin(x) + x*cos(x))*log(x) - ----------------------|*e
| 2 \ x / x |
\ x /
$$x^{e^{x \cos{\left(x \right)}}} \left(\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \log{\left(x \right)} - \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \right)} + \left(\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)} - \frac{1}{x}\right)^{2} e^{x \cos{\left(x \right)}} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x} - \frac{1}{x^{2}}\right) e^{x \cos{\left(x \right)}}$$
Tercera derivada
[src]
/ x*cos(x)\ / 3 2 \
\e / |2 / 1 \ 2*x*cos(x) 3 3*(2*sin(x) + x*cos(x)) 3*(-cos(x) + x*sin(x)) 3*(-cos(x) + x*sin(x)) / 1 \ /1 2 2*(-cos(x) + x*sin(x))\ x*cos(x) | x*cos(x)
x *|-- + (-3*cos(x) + x*sin(x))*log(x) - |- - + (-cos(x) + x*sin(x))*log(x)| *e - (-cos(x) + x*sin(x)) *log(x) - ----------------------- + ----------------------- + ---------------------- + 3*|- - + (-cos(x) + x*sin(x))*log(x)|*|-- + (2*sin(x) + x*cos(x))*log(x) - (-cos(x) + x*sin(x)) *log(x) + ----------------------|*e + 3*(-cos(x) + x*sin(x))*(2*sin(x) + x*cos(x))*log(x)|*e
| 3 \ x / x x 2 \ x / | 2 x | |
\x x \x / /
$$x^{e^{x \cos{\left(x \right)}}} \left(\left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) \log{\left(x \right)} - \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{3} \log{\left(x \right)} + 3 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \right)} - \left(\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)} - \frac{1}{x}\right)^{3} e^{2 x \cos{\left(x \right)}} + 3 \left(\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)} - \frac{1}{x}\right) \left(- \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \log{\left(x \right)} + \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \right)} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x} + \frac{1}{x^{2}}\right) e^{x \cos{\left(x \right)}} + \frac{3 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{x} - \frac{3 \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)}{x} + \frac{3 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x^{2}} + \frac{2}{x^{3}}\right) e^{x \cos{\left(x \right)}}$$