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^(7/6)
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Derivada de x^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Expresiones idénticas
- (xsinx)^(lnxsinx)
- (x seno de x) en el grado (lnx seno de x)
- (xsinx)(lnxsinx)
- xsinxlnxsinx
- xsinx^lnxsinx
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Expresiones con funciones
- xsinx
- xsinx*e^x
- xsinxe^(2x)
- xsinx-cosx
- xsinx+cisx
- xsinx+cosx-5/8*sinx
Derivada de (xsinx)^(lnxsinx)
Solución
Ha introducido
[src]
log(x)*sin(x) (x*sin(x))
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)} \sin{\left(x \right)}}$$
(x*sin(x))^(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]
log(x)*sin(x) //sin(x) \ (x*cos(x) + sin(x))*log(x)\
(x*sin(x)) *||------ + cos(x)*log(x)|*log(x*sin(x)) + --------------------------|
\\ x / x /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)} \sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \sin{\left(x \right)} \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x}\right)$$
Segunda derivada
[src]
/ /sin(x) \\
| 2 (x*cos(x) + sin(x))*|------ + cos(x)*log(x)||
log(x)*sin(x) |//sin(x) \ (x*cos(x) + sin(x))*log(x)\ x*cos(x) + sin(x) /sin(x) 2*cos(x)\ (-2*cos(x) + x*sin(x))*log(x) (x*cos(x) + sin(x))*log(x) \ x /|
(x*sin(x)) *|||------ + cos(x)*log(x)|*log(x*sin(x)) + --------------------------| + ----------------- - |------ + log(x)*sin(x) - --------|*log(x*sin(x)) - ----------------------------- - -------------------------- + --------------------------------------------|
|\\ x / x / 2 | 2 x | x 2 x*sin(x) |
\ x \ x / x /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)} \sin{\left(x \right)}} \left(\left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \sin{\left(x \right)} \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x}\right)^{2} - \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(x \sin{\left(x \right)} \right)} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{x} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x^{2}} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x^{2}}\right)$$
Tercera derivada
[src]
/ /sin(x) 2*cos(x)\ \
| / /sin(x) \\ /sin(x) \ /sin(x) \ 2*(x*cos(x) + sin(x))*|------ + log(x)*sin(x) - --------| /sin(x) \ |
| 3 | (x*cos(x) + sin(x))*|------ + cos(x)*log(x)|| (-2*cos(x) + x*sin(x))*|------ + cos(x)*log(x)| (x*cos(x) + sin(x))*|------ + cos(x)*log(x)| | 2 x | (x*cos(x) + sin(x))*|------ + cos(x)*log(x)|*cos(x)|
log(x)*sin(x) |//sin(x) \ (x*cos(x) + sin(x))*log(x)\ / 2*sin(x) 3*sin(x) 3*cos(x)\ 3*(x*cos(x) + sin(x)) //sin(x) \ (x*cos(x) + sin(x))*log(x)\ |/sin(x) 2*cos(x)\ x*cos(x) + sin(x) (-2*cos(x) + x*sin(x))*log(x) (x*cos(x) + sin(x))*log(x) \ x /| 2*(-2*cos(x) + x*sin(x)) (3*sin(x) + x*cos(x))*log(x) 2*(x*cos(x) + sin(x))*log(x) 2*(-2*cos(x) + x*sin(x))*log(x) \ x / \ x / \ x / \ x / |
(x*sin(x)) *|||------ + cos(x)*log(x)|*log(x*sin(x)) + --------------------------| - |cos(x)*log(x) - -------- + -------- + --------|*log(x*sin(x)) - --------------------- - 3*||------ + cos(x)*log(x)|*log(x*sin(x)) + --------------------------|*||------ + log(x)*sin(x) - --------|*log(x*sin(x)) - ----------------- + ----------------------------- + -------------------------- - --------------------------------------------| - ------------------------ - ---------------------------- + ---------------------------- + ------------------------------- - ----------------------------------------------- - -------------------------------------------- - --------------------------------------------------------- - ---------------------------------------------------|
|\\ x / x / | 3 x 2 | 3 \\ x / x / || 2 x | 2 x 2 x*sin(x) | 2 x 3 2 x*sin(x) 2 x*sin(x) 2 |
\ \ x x / x \\ x / x x / x x x x *sin(x) x*sin (x) /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)} \sin{\left(x \right)}} \left(\left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \sin{\left(x \right)} \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x}\right)^{3} - 3 \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \sin{\left(x \right)} \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x}\right) \left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(x \sin{\left(x \right)} \right)} + \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{x} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x^{2}} - \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x^{2}}\right) - \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{3 \cos{\left(x \right)}}{x^{2}} - \frac{2 \sin{\left(x \right)}}{x^{3}}\right) \log{\left(x \sin{\left(x \right)} \right)} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\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(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right)}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x \right)}}{x} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{x^{2}} - \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{x^{2}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{x^{2} \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x^{3}} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x^{3}}\right)$$
Gráfico