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/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- (xsinx)^(8ln(x-sinx))
- (x seno de x) en el grado (8ln(x menos seno de x))
- (xsinx)(8ln(x-sinx))
- xsinx8lnx-sinx
- xsinx^8lnx-sinx
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Expresiones semejantes
- (xsinx)^(8ln(x+sinx))
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Expresiones con funciones
- xsinx
- xsinx/cosx
- xsinx+cos
- xsinx-50
- xsinx^2
- xsinx+1/2*cos^2x
Derivada de (xsinx)^(8ln(x-sinx))
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)) /8*(1 - cos(x))*log(x*sin(x)) 8*(x*cos(x) + sin(x))*log(x - sin(x))\
(x*sin(x)) *|---------------------------- + -------------------------------------|
\ x - sin(x) x*sin(x) /
$$\left(x \sin{\left(x \right)}\right)^{8 \log{\left(x - \sin{\left(x \right)} \right)}} \left(\frac{8 \left(1 - \cos{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)}}{x - \sin{\left(x \right)}} + \frac{8 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}}\right)$$
Segunda derivada
[src]
/ 2 2 \
8*log(x - sin(x)) | /(-1 + cos(x))*log(x*sin(x)) (x*cos(x) + sin(x))*log(x - sin(x))\ log(x*sin(x))*sin(x) (-1 + cos(x)) *log(x*sin(x)) (-2*cos(x) + x*sin(x))*log(x - sin(x)) (x*cos(x) + sin(x))*log(x - sin(x)) (x*cos(x) + sin(x))*cos(x)*log(x - sin(x)) 2*(-1 + cos(x))*(x*cos(x) + sin(x))|
8*(x*sin(x)) *|8*|--------------------------- - -----------------------------------| + -------------------- - ---------------------------- - -------------------------------------- - ----------------------------------- - ------------------------------------------ - -----------------------------------|
| \ x - sin(x) x*sin(x) / x - sin(x) 2 x*sin(x) 2 2 x*(x - sin(x))*sin(x) |
\ (x - sin(x)) x *sin(x) x*sin (x) /
$$8 \left(x \sin{\left(x \right)}\right)^{8 \log{\left(x - \sin{\left(x \right)} \right)}} \left(8 \left(\frac{\left(\cos{\left(x \right)} - 1\right) \log{\left(x \sin{\left(x \right)} \right)}}{x - \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}}\right)^{2} + \frac{\log{\left(x \sin{\left(x \right)} \right)} \sin{\left(x \right)}}{x - \sin{\left(x \right)}} - \frac{\left(\cos{\left(x \right)} - 1\right)^{2} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x - \sin{\left(x \right)}\right)^{2}} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right)}{x \left(x - \sin{\left(x \right)}\right) \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x^{2} \sin{\left(x \right)}}\right)$$
Tercera derivada
[src]
/ 3 / 2 \ 3 2 2 \
8*log(x - sin(x)) | /(-1 + cos(x))*log(x*sin(x)) (x*cos(x) + sin(x))*log(x - sin(x))\ /(-1 + cos(x))*log(x*sin(x)) (x*cos(x) + sin(x))*log(x - sin(x))\ |(-1 + cos(x)) *log(x*sin(x)) log(x*sin(x))*sin(x) (-2*cos(x) + x*sin(x))*log(x - sin(x)) (x*cos(x) + sin(x))*log(x - sin(x)) (x*cos(x) + sin(x))*cos(x)*log(x - sin(x)) 2*(-1 + cos(x))*(x*cos(x) + sin(x))| cos(x)*log(x*sin(x)) 2*(-1 + cos(x)) *log(x*sin(x)) 3*(x*cos(x) + sin(x)) (x*cos(x) + sin(x))*log(x - sin(x)) (3*sin(x) + x*cos(x))*log(x - sin(x)) 2*(x*cos(x) + sin(x))*log(x - sin(x)) 2*(-2*cos(x) + x*sin(x))*log(x - sin(x)) 3*(-1 + cos(x))*log(x*sin(x))*sin(x) 3*(-1 + cos(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)) 2*(x*cos(x) + sin(x))*cos(x)*log(x - sin(x)) 3*(-1 + cos(x))*(-2*cos(x) + x*sin(x)) 3*(-1 + cos(x))*(x*cos(x) + sin(x)) 3*(-1 + cos(x))*(x*cos(x) + sin(x))*cos(x)|
8*(x*sin(x)) *|- 64*|--------------------------- - -----------------------------------| + 24*|--------------------------- - -----------------------------------|*|---------------------------- - -------------------- + -------------------------------------- + ----------------------------------- + ------------------------------------------ + -----------------------------------| + -------------------- - ------------------------------ + --------------------- + ----------------------------------- - ------------------------------------- + ------------------------------------- + ---------------------------------------- + ------------------------------------ - ------------------------------------ + --------------------------------------------- + ----------------------------------------------- + -------------------------------------------- + -------------------------------------- + ----------------------------------- + ------------------------------------------|
| \ x - sin(x) x*sin(x) / \ x - sin(x) x*sin(x) / | 2 x - sin(x) x*sin(x) 2 2 x*(x - sin(x))*sin(x) | x - sin(x) 3 x*(x - sin(x)) x*sin(x) x*sin(x) 3 2 2 2 3 2 2 2 x*(x - sin(x))*sin(x) 2 2 |
\ \ (x - sin(x)) x *sin(x) x*sin (x) / (x - sin(x)) x *sin(x) x *sin(x) (x - sin(x)) x*(x - sin(x)) *sin(x) x*sin (x) x*sin (x) x *sin (x) x *(x - sin(x))*sin(x) x*(x - sin(x))*sin (x) /
$$8 \left(x \sin{\left(x \right)}\right)^{8 \log{\left(x - \sin{\left(x \right)} \right)}} \left(- 64 \left(\frac{\left(\cos{\left(x \right)} - 1\right) \log{\left(x \sin{\left(x \right)} \right)}}{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 \sin{\left(x \right)}}\right)^{3} + 24 \left(\frac{\left(\cos{\left(x \right)} - 1\right) \log{\left(x \sin{\left(x \right)} \right)}}{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 \sin{\left(x \right)}}\right) \left(- \frac{\log{\left(x \sin{\left(x \right)} \right)} \sin{\left(x \right)}}{x - \sin{\left(x \right)}} + \frac{\left(\cos{\left(x \right)} - 1\right)^{2} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x - \sin{\left(x \right)}\right)^{2}} + \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{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)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right)}{x \left(x - \sin{\left(x \right)}\right) \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^{2} \sin{\left(x \right)}}\right) + \frac{\log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x - \sin{\left(x \right)}} + \frac{3 \left(\cos{\left(x \right)} - 1\right) \log{\left(x \sin{\left(x \right)} \right)} \sin{\left(x \right)}}{\left(x - \sin{\left(x \right)}\right)^{2}} - \frac{2 \left(\cos{\left(x \right)} - 1\right)^{3} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x - \sin{\left(x \right)}\right)^{3}} + \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)}}{x \sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \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)} \cos^{2}{\left(x \right)}}{x \sin^{3}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}} + \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right)}{x \left(x - \sin{\left(x \right)}\right) \sin{\left(x \right)}} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right) \cos{\left(x \right)}}{x \left(x - \sin{\left(x \right)}\right) \sin^{2}{\left(x \right)}} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \left(x - \sin{\left(x \right)}\right)} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right)^{2}}{x \left(x - \sin{\left(x \right)}\right)^{2} \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^{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)} \cos{\left(x \right)}}{x^{2} \sin^{2}{\left(x \right)}} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right)}{x^{2} \left(x - \sin{\left(x \right)}\right) \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^{3} \sin{\left(x \right)}}\right)$$
Gráfico