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^-(4/5)
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=(sinx)^x^cosx
- y es igual a ( seno de x) en el grado x en el grado coseno de x
- y=(sinx)xcosx
- y=sinxxcosx
- y=sinx^x^cosx
Derivada de y=(sinx)^x^cosx
Solución
Ha introducido
[src]
/ cos(x)\
\x /
(sin(x))
$$\sin^{x^{\cos{\left(x \right)}}}{\left(x \right)}$$
sin(x)^(x^cos(x))
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) \
\x / |x *cos(x) cos(x) /cos(x) \ |
(sin(x)) *|-------------- + x *|------ - log(x)*sin(x)|*log(sin(x))|
\ sin(x) \ x / /
$$\left(x^{\cos{\left(x \right)}} \left(- \log{\left(x \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{x^{\cos{\left(x \right)}} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{x^{\cos{\left(x \right)}}}{\left(x \right)}$$
Segunda derivada
[src]
/ / cos(x)\ \
/ cos(x)\ | 2 2 2 2*|log(x)*sin(x) - ------|*cos(x)|
cos(x) \x / | cos(x) // cos(x)\ cos(x)\ / cos(x)\ cos (x) /cos(x) 2*sin(x)\ \ x / |
x *(sin(x)) *|-1 + x *||log(x)*sin(x) - ------|*log(sin(x)) - ------| + |log(x)*sin(x) - ------| *log(sin(x)) - ------- - |------ + cos(x)*log(x) + --------|*log(sin(x)) - ---------------------------------|
| \\ x / sin(x)/ \ x / 2 | 2 x | sin(x) |
\ sin (x) \ x / /
$$x^{\cos{\left(x \right)}} \left(x^{\cos{\left(x \right)}} \left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} + \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{2} \log{\left(\sin{\left(x \right)} \right)} - \frac{2 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \log{\left(\sin{\left(x \right)} \right)} - 1 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{x^{\cos{\left(x \right)}}}{\left(x \right)}$$
Tercera derivada
[src]
/ /cos(x) 2*sin(x)\ 2 \
| 3*|------ + cos(x)*log(x) + --------|*cos(x) / / cos(x)\ \ / cos(x)\ 2 / cos(x)\ |
/ cos(x)\ | 3 3 3 | 2 x | | 2 2 2*|log(x)*sin(x) - ------|*cos(x)| 3*|log(x)*sin(x) - ------| *cos(x) 3*cos (x)*|log(x)*sin(x) - ------| |
cos(x) \x / |/ 3*cos(x) 2*cos(x) 3*sin(x)\ 2*cos(x) // cos(x)\ cos(x)\ / cos(x)\ 3*cos(x) 2*cos (x) 2*cos(x) \ x / cos(x) // cos(x)\ cos(x)\ | cos (x) /cos(x) 2*sin(x)\ / cos(x)\ \ x / | \ x / \ x / / cos(x)\ /cos(x) 2*sin(x)\ |
x *(sin(x)) *||log(x)*sin(x) - -------- + -------- + --------|*log(sin(x)) - x *||log(x)*sin(x) - ------|*log(sin(x)) - ------| - |log(x)*sin(x) - ------| *log(sin(x)) - -------- + --------- + -------- + 3*log(x)*sin(x) - -------------------------------------------- + 3*x *||log(x)*sin(x) - ------|*log(sin(x)) - ------|*|1 + ------- + |------ + cos(x)*log(x) + --------|*log(sin(x)) - |log(x)*sin(x) - ------| *log(sin(x)) + ---------------------------------| + ---------------------------------- + ---------------------------------- + 3*|log(x)*sin(x) - ------|*|------ + cos(x)*log(x) + --------|*log(sin(x))|
|| x 3 2 | \\ x / sin(x)/ \ x / x 3 sin(x) sin(x) \\ x / sin(x)/ | 2 | 2 x | \ x / sin(x) | sin(x) 2 \ x / | 2 x | |
\\ x x / sin (x) \ sin (x) \ x / / sin (x) \ x / /
$$x^{\cos{\left(x \right)}} \left(- x^{2 \cos{\left(x \right)}} \left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} + 3 x^{\cos{\left(x \right)}} \left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(- \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{2} \log{\left(\sin{\left(x \right)} \right)} + \frac{2 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \log{\left(\sin{\left(x \right)} \right)} + 1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) - \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{3} \log{\left(\sin{\left(x \right)} \right)} + \frac{3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + 3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x} + \frac{3 \sin{\left(x \right)}}{x^{2}} + \frac{2 \cos{\left(x \right)}}{x^{3}}\right) \log{\left(\sin{\left(x \right)} \right)} + 3 \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x}\right) \sin^{x^{\cos{\left(x \right)}}}{\left(x \right)}$$
Gráfico