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 x^4/3-x
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Derivada de x^-4/5
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Derivada de x=1
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Derivada de x^2*2^x
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Expresiones idénticas
- y=e^cos^xsen^x
- y es igual a e en el grado coseno de en el grado xsen en el grado x
- y=ecosxsenx
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Expresiones con funciones
- Coseno cos
- cos(3x^2+2)
- xsen
- xsen(p/x)
Derivada de y=e^cos^xsen^x
Solución
Ha introducido
[src]
/ / x\\ | \x /| \(cos(sin(x))) / E
$$e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}}$$
E^(cos(sin(x))^(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 \ | \x /|
\x / | x x *cos(x)*sin(sin(x))| \(cos(sin(x))) /
(cos(sin(x))) *|x *(1 + log(x))*log(cos(sin(x))) - ---------------------|*e
\ cos(sin(x)) /
$$\left(x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{x^{x} \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right) e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}$$
Segunda derivada
[src]
/ / x\\
/ x\ / 2 2 / x\ 2 2 \ | \x /|
x \x / | 2 log(cos(sin(x))) x / cos(x)*sin(sin(x))\ 2 x / cos(x)*sin(sin(x))\ \x / sin(x)*sin(sin(x)) cos (x)*sin (sin(x)) 2*(1 + log(x))*cos(x)*sin(sin(x))| \(cos(sin(x))) /
x *(cos(sin(x))) *|- cos (x) + ---------------- + x *|(1 + log(x))*log(cos(sin(x))) - ------------------| + (1 + log(x)) *log(cos(sin(x))) + x *|(1 + log(x))*log(cos(sin(x))) - ------------------| *(cos(sin(x))) + ------------------ - -------------------- - ---------------------------------|*e
| x \ cos(sin(x)) / \ cos(sin(x)) / cos(sin(x)) 2 cos(sin(x)) |
\ cos (sin(x)) /
$$x^{x} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{2} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{2} + \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{2 \left(\log{\left(x \right)} + 1\right) \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{\sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{\sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - \cos^{2}{\left(x \right)} + \frac{\log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right) e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}$$
Tercera derivada
[src]
/ / x\\
/ x\ / 3 3 x 3 3 3 / 2 2 \ 3 / x\ 2 2 2 / x\ / 2 2 \ 2 \ | \x /|
x \x / | 2*x / cos(x)*sin(sin(x))\ 3 log(cos(sin(x))) 2 2*x / cos(x)*sin(sin(x))\ 2*x cos(x)*sin(sin(x)) 2*cos (x)*sin(sin(x)) 2*cos (x)*sin (sin(x)) 3*(1 + log(x))*log(cos(sin(x))) x / cos(x)*sin(sin(x))\ | 2 log(cos(sin(x))) 2 sin(x)*sin(sin(x)) cos (x)*sin (sin(x)) 2*(1 + log(x))*cos(x)*sin(sin(x))| 2*x / cos(x)*sin(sin(x))\ \x / 3*cos(x)*sin(sin(x)) 3*(1 + log(x)) *cos(x)*sin(sin(x)) 3*cos (x)*sin (sin(x))*(1 + log(x)) x \x / / cos(x)*sin(sin(x))\ | 2 log(cos(sin(x))) 2 sin(x)*sin(sin(x)) cos (x)*sin (sin(x)) 2*(1 + log(x))*cos(x)*sin(sin(x))| 3*(1 + log(x))*sin(x)*sin(sin(x)) 3*sin (sin(x))*cos(x)*sin(x)| \(cos(sin(x))) /
x *(cos(sin(x))) *|x *|(1 + log(x))*log(cos(sin(x))) - ------------------| + (1 + log(x)) *log(cos(sin(x))) - ---------------- - 3*cos (x)*(1 + log(x)) + 3*cos(x)*sin(x) + x *|(1 + log(x))*log(cos(sin(x))) - ------------------| *(cos(sin(x))) + ------------------ - --------------------- - ---------------------- + ------------------------------- + 3*x *|(1 + log(x))*log(cos(sin(x))) - ------------------|*|- cos (x) + ---------------- + (1 + log(x)) *log(cos(sin(x))) + ------------------ - -------------------- - ---------------------------------| + 3*x *|(1 + log(x))*log(cos(sin(x))) - ------------------| *(cos(sin(x))) - -------------------- - ---------------------------------- - ----------------------------------- + 3*x *(cos(sin(x))) *|(1 + log(x))*log(cos(sin(x))) - ------------------|*|- cos (x) + ---------------- + (1 + log(x)) *log(cos(sin(x))) + ------------------ - -------------------- - ---------------------------------| + --------------------------------- + ----------------------------|*e
| \ cos(sin(x)) / 2 \ cos(sin(x)) / cos(sin(x)) cos(sin(x)) 3 x \ cos(sin(x)) / | x cos(sin(x)) 2 cos(sin(x)) | \ cos(sin(x)) / x*cos(sin(x)) cos(sin(x)) 2 \ cos(sin(x)) / | x cos(sin(x)) 2 cos(sin(x)) | cos(sin(x)) 2 |
\ x cos (sin(x)) \ cos (sin(x)) / cos (sin(x)) \ cos (sin(x)) / cos (sin(x)) /
$$x^{x} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{3} \cos^{2 x^{x}}{\left(\sin{\left(x \right)} \right)} + 3 x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{3} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)} + x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{3} + 3 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right) \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{2 \left(\log{\left(x \right)} + 1\right) \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{\sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{\sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - \cos^{2}{\left(x \right)} + \frac{\log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right) \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)} + 3 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right) \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{2 \left(\log{\left(x \right)} + 1\right) \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{\sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{\sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - \cos^{2}{\left(x \right)} + \frac{\log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right) + \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{3 \left(\log{\left(x \right)} + 1\right)^{2} \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{3 \left(\log{\left(x \right)} + 1\right) \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{3 \left(\log{\left(x \right)} + 1\right) \sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - 3 \left(\log{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)} + \frac{3 \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 \sin{\left(x \right)} \cos{\left(x \right)} - \frac{2 \sin^{3}{\left(\sin{\left(x \right)} \right)} \cos^{3}{\left(x \right)}}{\cos^{3}{\left(\sin{\left(x \right)} \right)}} - \frac{2 \sin{\left(\sin{\left(x \right)} \right)} \cos^{3}{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{3 \left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x} - \frac{3 \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \cos{\left(\sin{\left(x \right)} \right)}} - \frac{\log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x^{2}}\right) e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}$$
Gráfico