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 v
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Derivada de (x+12)e^(12-x)
- Derivada de u/v
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Derivada de x^(1/10)
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Expresiones idénticas
- x(sinx)^(ln(xsinx))
- x( seno de x) en el grado (ln(x seno de x))
- x(sinx)(ln(xsinx))
- xsinxlnxsinx
- xsinx^lnxsinx
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Expresiones con funciones
- ln
- ln(1+e^-x)
- ln2*((((1+cos(2*x))^3)^(1/2)))
- ln((x+a)^0.5)
- xsinx
- xsinx-5
- xsinx+5lnx
Derivada de x(sinx)^(ln(xsinx))
Solución
Ha introducido
[src]
log(x*sin(x)) x*sin (x)
$$x \sin^{\log{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)}$$
x*sin(x)^log(x*sin(x))
Solución detallada
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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Según el principio, aplicamos: tenemos
; calculamos :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de:
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Respuesta:
Primera derivada
[src]
log(x*sin(x)) log(x*sin(x)) /cos(x)*log(x*sin(x)) (x*cos(x) + sin(x))*log(sin(x))\
sin (x) + x*sin (x)*|-------------------- + -------------------------------|
\ sin(x) x*sin(x) /
$$x \left(\frac{\log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}}\right) \sin^{\log{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)} + \sin^{\log{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ / 2 \ \
| | / (x*cos(x) + sin(x))*log(sin(x))\ | / (x*cos(x) + sin(x))*log(sin(x))\|
| | |cos(x)*log(x*sin(x)) + -------------------------------| 2 | 2*|cos(x)*log(x*sin(x)) + -------------------------------||
log(x*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)) | \ x /|
sin (x)*|- x*|- --------------------------------------------------------- + --------------------- + ---------------------------------- + ------------------------------- - ---------------------------- + -------------------------------------- + log(x*sin(x))| + ----------------------------------------------------------|
| | 2 2 x*sin(x) 2 2 2 | sin(x) |
\ \ sin (x) sin (x) x *sin(x) x*sin (x) x*sin (x) / /
$$\left(- x \left(- \frac{\left(\log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x}\right)^{2}}{\sin^{2}{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)} + \frac{\log{\left(x \sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{2} \sin{\left(x \right)}}\right) + \frac{2 \left(\log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)}}{x}\right)}{\sin{\left(x \right)}}\right) \sin^{\log{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ / 3 \ \
| |/ (x*cos(x) + sin(x))*log(sin(x))\ | |
| ||cos(x)*log(x*sin(x)) + -------------------------------| / 2 \ 3 2 2 | |
| 2 |\ x / 3*(x*cos(x) + 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)) | (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))| |
| / (x*cos(x) + sin(x))*log(sin(x))\ x*|--------------------------------------------------------- - --------------------- - 3*|cos(x)*log(x*sin(x)) + -------------------------------|*|--------------------- + ---------------------------------- + ------------------------------- - ---------------------------- + -------------------------------------- + log(x*sin(x))| + 2*cos(x)*log(x*sin(x)) + ------------------------------- - --------------------------------- + --------------------------------- + ------------------------------------ + ----------------------- - ----------------------------- - ------------------------------- - ---------------------------- + ----------------------------------------- + ------------------------------------------- + ----------------------------------------| |
| 3*|cos(x)*log(x*sin(x)) + -------------------------------| | 2 x \ x / | 2 x*sin(x) 2 2 2 | x x 3 2 2 2 x*sin(x) 2 2 x*sin(x) 2 | 2 |
log(x*sin(x)) | \ x / \ sin (x) \ sin (x) x *sin(x) x*sin (x) x*sin (x) / x x sin (x) x*sin (x) x *sin(x) x*sin (x) x *sin(x) / 3*cos (x)*log(x*sin(x)) 3*(-2*cos(x) + x*sin(x))*log(sin(x)) 3*(x*cos(x) + sin(x))*log(sin(x)) 6*(x*cos(x) + sin(x))*cos(x) 3*(x*cos(x) + sin(x))*cos(x)*log(sin(x))|
sin (x)*|-3*log(x*sin(x)) + ----------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------- - ------------------------------------ - --------------------------------- + ---------------------------- - ----------------------------------------|
| 2 sin(x) 2 x*sin(x) 2 2 2 |
\ sin (x) sin (x) x *sin(x) x*sin (x) x*sin (x) /
$$\left(\frac{x \left(\frac{\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)}} - 3 \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)}} + \frac{3 \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)}} - 3 \log{\left(x \sin{\left(x \right)} \right)} - \frac{3 \log{\left(x \sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{3 \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{3 \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{6 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{3 \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) \sin^{\log{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)}$$
Gráfico