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 e^((3*x)^2)
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Derivada de d/dx(x)
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Derivada de (cos(x))^x^2
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Derivada de (8*x-15)^5
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Expresiones idénticas
- y=(x*sin(x))^(8lnsin(x))
- y es igual a (x multiplicar por seno de (x)) en el grado (8ln seno de (x))
- y=(x*sin(x))(8lnsin(x))
- y=x*sinx8lnsinx
- y=(xsin(x))^(8lnsin(x))
- y=(xsin(x))(8lnsin(x))
- y=xsinx8lnsinx
- y=xsinx^8lnsinx
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Expresiones semejantes
- y=(x*sinx)^(8lnsinx)
Derivada de y=(x*sin(x))^(8lnsin(x))
Solución
Ha introducido
[src]
8*log(sin(x)) (x*sin(x))
$$\left(x \sin{\left(x \right)}\right)^{8 \log{\left(\sin{\left(x \right)} \right)}}$$
(x*sin(x))^(8*log(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(sin(x)) /8*cos(x)*log(x*sin(x)) 8*(x*cos(x) + sin(x))*log(sin(x))\
(x*sin(x)) *|---------------------- + ---------------------------------|
\ sin(x) x*sin(x) /
$$\left(x \sin{\left(x \right)}\right)^{8 \log{\left(\sin{\left(x \right)} \right)}} \left(\frac{8 \log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{8 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}}\right)$$
Segunda derivada
[src]
/ 2 \
| / (x*cos(x) + sin(x))*log(sin(x))\ |
| 8*|cos(x)*log(x*sin(x)) + -------------------------------| 2 |
8*log(sin(x)) | \ x / cos (x)*log(x*sin(x)) (-2*cos(x) + x*sin(x))*log(sin(x)) (x*cos(x) + sin(x))*log(sin(x)) 2*(x*cos(x) + sin(x))*cos(x) (x*cos(x) + sin(x))*cos(x)*log(sin(x))|
8*(x*sin(x)) *|-log(x*sin(x)) + ----------------------------------------------------------- - --------------------- - ---------------------------------- - ------------------------------- + ---------------------------- - --------------------------------------|
| 2 2 x*sin(x) 2 2 2 |
\ sin (x) sin (x) x *sin(x) x*sin (x) x*sin (x) /
$$8 \left(x \sin{\left(x \right)}\right)^{8 \log{\left(\sin{\left(x \right)} \right)}} \left(\frac{8 \left(\log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x}\right)^{2}}{\sin^{2}{\left(x \right)}} - \log{\left(x \sin{\left(x \right)} \right)} - \frac{\log{\left(x \sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{2} \sin{\left(x \right)}}\right)$$
Tercera derivada
[src]
/ 3 \
| / (x*cos(x) + sin(x))*log(sin(x))\ |
| / 2 \ 64*|cos(x)*log(x*sin(x)) + -------------------------------| 3 2 2 |
8*log(sin(x)) | / (x*cos(x) + sin(x))*log(sin(x))\ |cos (x)*log(x*sin(x)) (-2*cos(x) + x*sin(x))*log(sin(x)) (x*cos(x) + sin(x))*log(sin(x)) 2*(x*cos(x) + sin(x))*cos(x) (x*cos(x) + sin(x))*cos(x)*log(sin(x)) | 3*(x*cos(x) + sin(x)) \ x / (x*cos(x) + sin(x))*log(sin(x)) (3*sin(x) + x*cos(x))*log(sin(x)) 2*(x*cos(x) + sin(x))*log(sin(x)) 2*(-2*cos(x) + x*sin(x))*log(sin(x)) 2*cos (x)*log(x*sin(x)) 6*cos (x)*(x*cos(x) + sin(x)) 3*(-2*cos(x) + x*sin(x))*cos(x) 3*(x*cos(x) + sin(x))*cos(x) 2*cos (x)*(x*cos(x) + sin(x))*log(sin(x)) 2*(-2*cos(x) + x*sin(x))*cos(x)*log(sin(x)) 2*(x*cos(x) + sin(x))*cos(x)*log(sin(x))|
8*(x*sin(x)) *|- 24*|cos(x)*log(x*sin(x)) + -------------------------------|*|--------------------- + ---------------------------------- + ------------------------------- - ---------------------------- + -------------------------------------- + log(x*sin(x))| - --------------------- + 2*cos(x)*log(x*sin(x)) + ------------------------------------------------------------ + ------------------------------- - --------------------------------- + --------------------------------- + ------------------------------------ + ----------------------- - ----------------------------- - ------------------------------- - ---------------------------- + ----------------------------------------- + ------------------------------------------- + ----------------------------------------|
| \ x / | 2 x*sin(x) 2 2 2 | x 2 x x 3 2 2 2 x*sin(x) 2 2 x*sin(x) 2 |
\ \ sin (x) x *sin(x) x*sin (x) x*sin (x) / sin (x) x x sin (x) x*sin (x) x *sin(x) x*sin (x) x *sin(x) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
sin(x)
$$\frac{8 \left(x \sin{\left(x \right)}\right)^{8 \log{\left(\sin{\left(x \right)} \right)}} \left(\frac{64 \left(\log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x}\right)^{3}}{\sin^{2}{\left(x \right)}} - 24 \left(\log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x}\right) \left(\log{\left(x \sin{\left(x \right)} \right)} + \frac{\log{\left(x \sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{2} \sin{\left(x \right)}}\right) + 2 \log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{2 \log{\left(x \sin{\left(x \right)} \right)} \cos^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x} - \frac{6 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{3}}\right)}{\sin{\left(x \right)}}$$