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:
-
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
- (xsin(x))^(8ln(xsin(x)))
- (x seno de (x)) en el grado (8ln(x seno de (x)))
- (xsin(x))(8ln(xsin(x)))
- xsinx8lnxsinx
- xsinx^8lnxsinx
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Expresiones semejantes
- (xsinx)^(8ln(xsinx))
- y=(xsin(x))^(8ln(xsin(x)))
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Expresiones con funciones
- xsin
- xsinx-xcosx
- xsinxe^(2x)
- xsinx-cosx
- xsinx+cisx
- xsin(x)+cos(x)-4sin(x)+5
- xsin
- xsinx-xcosx
- xsinxe^(2x)
- xsinx-cosx
- xsinx+cisx
- xsin(x)+cos(x)-4sin(x)+5
Derivada de (xsin(x))^(8ln(xsin(x)))
Solución
Ha introducido
[src]
8*log(x*sin(x)) (x*sin(x))
$$\left(x \sin{\left(x \right)}\right)^{8 \log{\left(x \sin{\left(x \right)} \right)}}$$
(x*sin(x))^(8*log(x*sin(x)))
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
8*log(x*sin(x))
16*(x*sin(x)) *(x*cos(x) + sin(x))*log(x*sin(x))
--------------------------------------------------------------
x*sin(x)
$$\frac{16 \left(x \sin{\left(x \right)}\right)^{8 \log{\left(x \sin{\left(x \right)} \right)}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}}$$
Segunda derivada
[src]
/ 2 2 2 \
8*log(x*sin(x)) | (x*cos(x) + sin(x)) (x*cos(x) + sin(x))*log(x*sin(x)) (x*cos(x) + sin(x))*cos(x)*log(x*sin(x)) 16*(x*cos(x) + sin(x)) *log (x*sin(x))|
16*(x*sin(x)) *|-(-2*cos(x) + x*sin(x))*log(x*sin(x)) + -------------------- - --------------------------------- - ---------------------------------------- + --------------------------------------|
\ x*sin(x) x sin(x) x*sin(x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x*sin(x)
$$\frac{16 \left(x \sin{\left(x \right)}\right)^{8 \log{\left(x \sin{\left(x \right)} \right)}} \left(- \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{16 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \log{\left(x \sin{\left(x \right)} \right)}^{2}}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2}}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)}}{x}\right)}{x \sin{\left(x \right)}}$$
Tercera derivada
[src]
/ 2 2 2 2 2 3 3 3 2 2 2 \
8*log(x*sin(x)) | 3*(x*cos(x) + sin(x)) 2*(-2*cos(x) + x*sin(x))*log(x*sin(x)) 2*(x*cos(x) + sin(x))*log(x*sin(x)) 48*(x*cos(x) + sin(x)) *log (x*sin(x)) 3*(x*cos(x) + sin(x)) *cos(x) 3*(-2*cos(x) + x*sin(x))*(x*cos(x) + sin(x)) 2*cos (x)*(x*cos(x) + sin(x))*log(x*sin(x)) 2*(-2*cos(x) + x*sin(x))*cos(x)*log(x*sin(x)) 48*(x*cos(x) + sin(x)) *log(x*sin(x)) 256*(x*cos(x) + sin(x)) *log (x*sin(x)) 48*(x*cos(x) + sin(x)) *log (x*sin(x))*cos(x) 48*log (x*sin(x))*(-2*cos(x) + x*sin(x))*(x*cos(x) + sin(x)) 2*(x*cos(x) + sin(x))*cos(x)*log(x*sin(x))|
16*(x*sin(x)) *|(x*cos(x) + sin(x))*log(x*sin(x)) - (3*sin(x) + x*cos(x))*log(x*sin(x)) - ---------------------- + -------------------------------------- + ----------------------------------- - -------------------------------------- - ----------------------------- - -------------------------------------------- + ------------------------------------------- + --------------------------------------------- + ------------------------------------- + --------------------------------------- - --------------------------------------------- - ------------------------------------------------------------ + ------------------------------------------|
| 2 x 2 2 2 x*sin(x) 2 sin(x) 2 2 2 2 2 x*sin(x) x*sin(x) |
\ x *sin(x) x x *sin(x) x*sin (x) sin (x) x *sin (x) x *sin (x) x*sin (x) /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x*sin(x)
$$\frac{16 \left(x \sin{\left(x \right)}\right)^{8 \log{\left(x \sin{\left(x \right)} \right)}} \left(\frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} - \frac{48 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)}^{2}}{x \sin{\left(x \right)}} - \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \sin{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)}}{x} - \frac{48 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \log{\left(x \sin{\left(x \right)} \right)}^{2} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{256 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{3} \log{\left(x \sin{\left(x \right)} \right)}^{3}}{x^{2} \sin^{2}{\left(x \right)}} + \frac{48 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{3} \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} \sin^{2}{\left(x \right)}} - \frac{48 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \log{\left(x \sin{\left(x \right)} \right)}^{2}}{x^{2} \sin{\left(x \right)}} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2}}{x^{2} \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)}}{x^{2}}\right)}{x \sin{\left(x \right)}}$$
Gráfico