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
- y=e^cossen^x
- y es igual a e en el grado coseno de sen en el grado x
- y=ecossenx
Derivada de y=e^cossen^x
Solución
Ha introducido
[src]
x cos (sin(x)) E
$$e^{\cos^{x}{\left(\sin{\left(x \right)} \right)}}$$
E^(cos(sin(x))^x)
Solución detallada
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Sustituimos .
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Derivado es.
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Luego se aplica una cadena de reglas. Multiplicamos por :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de la secuencia de reglas:
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Respuesta:
Primera derivada
[src]
x
x / x*cos(x)*sin(sin(x)) \ cos (sin(x))
cos (sin(x))*|- -------------------- + log(cos(sin(x)))|*e
\ cos(sin(x)) /
$$\left(- \frac{x \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}\right) e^{\cos^{x}{\left(\sin{\left(x \right)} \right)}} \cos^{x}{\left(\sin{\left(x \right)} \right)}$$
Segunda derivada
[src]
/ 2 2 2 2 \ x
x |/ x*cos(x)*sin(sin(x))\ / x*cos(x)*sin(sin(x))\ x 2 2*cos(x)*sin(sin(x)) x*sin(x)*sin(sin(x)) x*cos (x)*sin (sin(x))| cos (sin(x))
cos (sin(x))*||-log(cos(sin(x))) + --------------------| + |-log(cos(sin(x))) + --------------------| *cos (sin(x)) - x*cos (x) - -------------------- + -------------------- - ----------------------|*e
|\ cos(sin(x)) / \ cos(sin(x)) / cos(sin(x)) cos(sin(x)) 2 |
\ cos (sin(x)) /
$$\left(\frac{x \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{x \sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - x \cos^{2}{\left(x \right)} + \left(\frac{x \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}\right)^{2} \cos^{x}{\left(\sin{\left(x \right)} \right)} + \left(\frac{x \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}\right)^{2} - \frac{2 \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right) e^{\cos^{x}{\left(\sin{\left(x \right)} \right)}} \cos^{x}{\left(\sin{\left(x \right)} \right)}$$
Tercera derivada
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/ 3 3 3 / 2 2 \ 2 2 / 2 2 \ 3 3 3 2 \ x
x | / x*cos(x)*sin(sin(x))\ 2 / x*cos(x)*sin(sin(x))\ 2*x / x*cos(x)*sin(sin(x))\ x / x*cos(x)*sin(sin(x))\ | 2 2*cos(x)*sin(sin(x)) x*cos (x)*sin (sin(x)) x*sin(x)*sin(sin(x))| 3*cos (x)*sin (sin(x)) 3*sin(x)*sin(sin(x)) x / x*cos(x)*sin(sin(x))\ | 2 2*cos(x)*sin(sin(x)) x*cos (x)*sin (sin(x)) x*sin(x)*sin(sin(x))| x*cos(x)*sin(sin(x)) 2*x*cos (x)*sin(sin(x)) 2*x*cos (x)*sin (sin(x)) 3*x*sin (sin(x))*cos(x)*sin(x)| cos (sin(x))
cos (sin(x))*|- |-log(cos(sin(x))) + --------------------| - 3*cos (x) - |-log(cos(sin(x))) + --------------------| *cos (sin(x)) - 3*|-log(cos(sin(x))) + --------------------| *cos (sin(x)) + 3*|-log(cos(sin(x))) + --------------------|*|x*cos (x) + -------------------- + ---------------------- - --------------------| - ---------------------- + 3*x*cos(x)*sin(x) + -------------------- + 3*cos (sin(x))*|-log(cos(sin(x))) + --------------------|*|x*cos (x) + -------------------- + ---------------------- - --------------------| + -------------------- - ----------------------- - ------------------------ + ------------------------------|*e
| \ cos(sin(x)) / \ cos(sin(x)) / \ cos(sin(x)) / \ cos(sin(x)) / | cos(sin(x)) 2 cos(sin(x)) | 2 cos(sin(x)) \ cos(sin(x)) / | cos(sin(x)) 2 cos(sin(x)) | cos(sin(x)) cos(sin(x)) 3 2 |
\ \ cos (sin(x)) / cos (sin(x)) \ cos (sin(x)) / cos (sin(x)) cos (sin(x)) /
$$\left(\frac{3 x \sin{\left(x \right)} \sin^{2}{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} + 3 x \sin{\left(x \right)} \cos{\left(x \right)} - \frac{2 x \sin^{3}{\left(\sin{\left(x \right)} \right)} \cos^{3}{\left(x \right)}}{\cos^{3}{\left(\sin{\left(x \right)} \right)}} - \frac{2 x \sin{\left(\sin{\left(x \right)} \right)} \cos^{3}{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{x \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \left(\frac{x \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}\right)^{3} \cos^{2 x}{\left(\sin{\left(x \right)} \right)} - 3 \left(\frac{x \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}\right)^{3} \cos^{x}{\left(\sin{\left(x \right)} \right)} - \left(\frac{x \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}\right)^{3} + 3 \left(\frac{x \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}\right) \left(- \frac{x \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{x \sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} + x \cos^{2}{\left(x \right)} + \frac{2 \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right) \cos^{x}{\left(\sin{\left(x \right)} \right)} + 3 \left(\frac{x \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}\right) \left(- \frac{x \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{x \sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} + x \cos^{2}{\left(x \right)} + \frac{2 \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right) + \frac{3 \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{3 \sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - 3 \cos^{2}{\left(x \right)}\right) e^{\cos^{x}{\left(\sin{\left(x \right)} \right)}} \cos^{x}{\left(\sin{\left(x \right)} \right)}$$
Gráfico