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
-
¿Cómo usar?
- Derivada de:
-
Derivada de x^-3
-
Derivada de x*2
-
Derivada de x^4*sin(x)
-
Derivada de tan(x)*sin(x)
-
Expresiones idénticas
- (sin(x))^(cos(x))+(cos(x))^(sin(x))
- ( seno de (x)) en el grado ( coseno de (x)) más ( coseno de (x)) en el grado ( seno de (x))
- (sin(x))(cos(x))+(cos(x))(sin(x))
- sinxcosx+cosxsinx
- sinx^cosx+cosx^sinx
-
Expresiones semejantes
- (sin(x))^(cos(x))-(cos(x))^(sin(x))
- (sinx)^(cosx)+(cosx)^(sinx)
-
Expresiones con funciones
- Seno sin
- sin(x)-cos(x)
- sinx/1+cosx
- sin3x+cos3x
- sin^22x
- sinx*e^x
- Coseno cos
- cos(x)^(2)
- cos(x)^(4)
- cos(4*x)
- cos(x)/x
- cos(x)-log(x)
- Coseno cos
- cos(x)^(2)
- cos(x)^(4)
- cos(4*x)
- cos(x)/x
- cos(x)-log(x)
- Seno sin
- sin(x)-cos(x)
- sinx/1+cosx
- sin3x+cos3x
- sin^22x
- sinx*e^x
Derivada de (sin(x))^(cos(x))+(cos(x))^(sin(x))
Solución
Ha introducido
[src]
cos(x) sin(x) sin (x) + cos (x)
$$\sin^{\cos{\left(x \right)}}{\left(x \right)} + \cos^{\sin{\left(x \right)}}{\left(x \right)}$$
sin(x)^cos(x) + cos(x)^sin(x)
Solución detallada
-
diferenciamos miembro por miembro:
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de:
-
Respuesta:
Primera derivada
[src]
/ 2 \ / 2 \
sin(x) | sin (x)| cos(x) |cos (x) |
cos (x)*|cos(x)*log(cos(x)) - -------| + sin (x)*|------- - log(sin(x))*sin(x)|
\ cos(x)/ \ sin(x) /
$$\left(- \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)} + \left(\log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\right) \cos^{\sin{\left(x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
2 2
/ 2 \ / 2 \ / 2 \ / 2 \
| sin (x)| sin(x) | cos (x)| cos(x) sin(x) | sin (x) | cos(x) | cos (x) |
|cos(x)*log(cos(x)) - -------| *cos (x) + |log(sin(x))*sin(x) - -------| *sin (x) - cos (x)*|3 + ------- + log(cos(x))|*sin(x) - sin (x)*|3 + ------- + log(sin(x))|*cos(x)
\ cos(x)/ \ sin(x)/ | 2 | | 2 |
\ cos (x) / \ sin (x) /
$$\left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \sin^{\cos{\left(x \right)}}{\left(x \right)} + \left(\log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\right)^{2} \cos^{\sin{\left(x \right)}}{\left(x \right)} - \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)} \cos{\left(x \right)} - \left(\log{\left(\cos{\left(x \right)} \right)} + \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 3\right) \sin{\left(x \right)} \cos^{\sin{\left(x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
3 3
/ 2 \ / 2 4 \ / 2 \ / 2 4 \ / 2 \ / 2 \ / 2 \ / 2 \
| sin (x)| sin(x) cos(x) | 2*cos (x) 2*cos (x)| | cos (x)| cos(x) sin(x) | 2*sin (x) 2*sin (x)| sin(x) | sin (x)| | sin (x) | cos(x) | cos (x)| | cos (x) |
|cos(x)*log(cos(x)) - -------| *cos (x) + sin (x)*|3*sin(x) + log(sin(x))*sin(x) + --------- + ---------| - |log(sin(x))*sin(x) - -------| *sin (x) - cos (x)*|3*cos(x) + cos(x)*log(cos(x)) + --------- + ---------| - 3*cos (x)*|cos(x)*log(cos(x)) - -------|*|3 + ------- + log(cos(x))|*sin(x) + 3*sin (x)*|log(sin(x))*sin(x) - -------|*|3 + ------- + log(sin(x))|*cos(x)
\ cos(x)/ | sin(x) 3 | \ sin(x)/ | cos(x) 3 | \ cos(x)/ | 2 | \ sin(x)/ | 2 |
\ sin (x) / \ cos (x) / \ cos (x) / \ sin (x) /
$$- \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \sin^{\cos{\left(x \right)}}{\left(x \right)} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)} \cos{\left(x \right)} + \left(\log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\right)^{3} \cos^{\sin{\left(x \right)}}{\left(x \right)} - 3 \left(\log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\right) \left(\log{\left(\cos{\left(x \right)} \right)} + \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 3\right) \sin{\left(x \right)} \cos^{\sin{\left(x \right)}}{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + 3 \sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{4}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)} - \left(\log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{2 \sin^{4}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{2 \sin^{2}{\left(x \right)}}{\cos{\left(x \right)}} + 3 \cos{\left(x \right)}\right) \cos^{\sin{\left(x \right)}}{\left(x \right)}$$
Gráfico