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|x|
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Derivada de x^-7
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Derivada de f(x)=√x
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Derivada de (cosx)^x
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Expresiones idénticas
- x*sin(x)^(log(x)*sin(x))
- x multiplicar por seno de (x) en el grado ( logaritmo de (x) multiplicar por seno de (x))
- x*sin(x)(log(x)*sin(x))
- x*sinxlogx*sinx
- xsin(x)^(log(x)sin(x))
- xsin(x)(log(x)sin(x))
- xsinxlogxsinx
- xsinx^logxsinx
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Expresiones semejantes
- x*sinx^(log(x)*sinx)
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Expresiones con funciones
- Seno sin
- sin^2*2x
- sin(x)-x
- sin(x)/(x*cos(x))
- sin(x)/log(x)
- sin*x^2
- Logaritmo log
- log(x^2+2*x)
- log(t^2+1)
- log(1-t^2)
- log(x+4)^11
- logsinx
- Seno sin
- sin^2*2x
- sin(x)-x
- sin(x)/(x*cos(x))
- sin(x)/log(x)
- sin*x^2
Derivada de x*sin(x)^(log(x)*sin(x))
Solución
Ha introducido
[src]
log(x)*sin(x) x*sin (x)
$$x \sin^{\log{\left(x \right)} \sin{\left(x \right)}}{\left(x \right)}$$
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) //sin(x) \ \
sin (x) + x*sin (x)*||------ + cos(x)*log(x)|*log(sin(x)) + cos(x)*log(x)|
\\ x / /
$$x \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(x \right)} \cos{\left(x \right)}\right) \sin^{\log{\left(x \right)} \sin{\left(x \right)}}{\left(x \right)} + \sin^{\log{\left(x \right)} \sin{\left(x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ / /sin(x) \ \ \
| | 2 |------ + cos(x)*log(x)|*cos(x)| |
log(x)*sin(x) | |//sin(x) \ \ cos(x) /sin(x) 2*cos(x)\ \ x / | /sin(x) \ |
sin (x)*|x*|||------ + cos(x)*log(x)|*log(sin(x)) + cos(x)*log(x)| + ------ - |------ + log(x)*sin(x) - --------|*log(sin(x)) - log(x)*sin(x) + -------------------------------| + 2*|------ + cos(x)*log(x)|*log(sin(x)) + 2*cos(x)*log(x)|
| |\\ x / / x | 2 x | sin(x) | \ x / |
\ \ \ x / / /
$$\left(x \left(\left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(x \right)} \cos{\left(x \right)}\right)^{2} + \frac{\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(\sin{\left(x \right)} \right)} - \log{\left(x \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) + 2 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} + 2 \log{\left(x \right)} \cos{\left(x \right)}\right) \sin^{\log{\left(x \right)} \sin{\left(x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ / /sin(x) 2*cos(x)\ \ \
| | / /sin(x) \ \ 2 /sin(x) \ 2*|------ + log(x)*sin(x) - --------|*cos(x)| /sin(x) \ |
| 2 | 3 | |------ + cos(x)*log(x)|*cos(x)| cos (x)*|------ + cos(x)*log(x)| | 2 x | | 3*|------ + cos(x)*log(x)|*cos(x)|
log(x)*sin(x) | //sin(x) \ \ | //sin(x) \ \ cos(x) / 2*sin(x) 3*sin(x) 3*cos(x)\ //sin(x) \ \ |cos(x) /sin(x) 2*cos(x)\ \ x / | 3*sin(x) \ x / \ x / | /sin(x) 2*cos(x)\ 3*cos(x) \ x / |
sin (x)*|3*||------ + cos(x)*log(x)|*log(sin(x)) + cos(x)*log(x)| - x*|- ||------ + cos(x)*log(x)|*log(sin(x)) + cos(x)*log(x)| + ------ + |cos(x)*log(x) - -------- + -------- + --------|*log(sin(x)) - 3*||------ + cos(x)*log(x)|*log(sin(x)) + cos(x)*log(x)|*|------ - |------ + log(x)*sin(x) - --------|*log(sin(x)) - log(x)*sin(x) + -------------------------------| + 2*cos(x)*log(x) + -------- + -------------------------------- + --------------------------------------------| - 3*|------ + log(x)*sin(x) - --------|*log(sin(x)) - 3*log(x)*sin(x) + -------- + ---------------------------------|
| \\ x / / | \\ x / / 2 | 3 x 2 | \\ x / / | x | 2 x | sin(x) | x 2 sin(x) | | 2 x | x sin(x) |
\ \ x \ x x / \ \ x / / sin (x) / \ x / /
$$\left(- x \left(- \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(x \right)} \cos{\left(x \right)}\right)^{3} - 3 \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(x \right)} \cos{\left(x \right)}\right) \left(\frac{\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \cos{\left(x \right)}}{\sin{\left(x \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) \log{\left(\sin{\left(x \right)} \right)} - \log{\left(x \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) + \frac{\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{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) \cos{\left(x \right)}}{\sin{\left(x \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(\sin{\left(x \right)} \right)} + 2 \log{\left(x \right)} \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) + 3 \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(x \right)} \cos{\left(x \right)}\right)^{2} + \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - 3 \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(\sin{\left(x \right)} \right)} - 3 \log{\left(x \right)} \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{x}\right) \sin^{\log{\left(x \right)} \sin{\left(x \right)}}{\left(x \right)}$$
Gráfico