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 (4-3*x)^7
-
Derivada de 2^√x
-
Derivada de 3^(1/x)
-
Derivada de 2*x+8/x
-
Expresiones idénticas
- x*sin(x)^(sin(x*sin(x)))
- x multiplicar por seno de (x) en el grado ( seno de (x multiplicar por seno de (x)))
- x*sin(x)(sin(x*sin(x)))
- x*sinxsinx*sinx
- xsin(x)^(sin(xsin(x)))
- xsin(x)(sin(xsin(x)))
- xsinxsinxsinx
- xsinx^sinxsinx
-
Expresiones semejantes
- x*sinx^(sin(x*sinx))
-
Expresiones con funciones
- Seno sin
- sin(x)/5*x
- sin(x)^(6)
- sin(x/3+3)+2*x
- sin(x+2)
- sin(x)/2-cos(x)/2+10*e^(-x)
- Seno sin
- sin(x)/5*x
- sin(x)^(6)
- sin(x/3+3)+2*x
- sin(x+2)
- sin(x)/2-cos(x)/2+10*e^(-x)
- Seno sin
- sin(x)/5*x
- sin(x)^(6)
- sin(x/3+3)+2*x
- sin(x+2)
- sin(x)/2-cos(x)/2+10*e^(-x)
Derivada de x*sin(x)^(sin(x*sin(x)))
Solución
Ha introducido
[src]
sin(x*sin(x)) x*sin (x)
$$x \sin^{\sin{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)}$$
x*sin(x)^sin(x*sin(x))
Solución detallada
-
Se aplica la regla de la derivada de una multiplicación:
; calculamos :
-
Según el principio, aplicamos: tenemos
; calculamos :
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de:
-
Respuesta:
Primera derivada
[src]
sin(x*sin(x)) sin(x*sin(x)) /cos(x)*sin(x*sin(x)) \
sin (x) + x*sin (x)*|-------------------- + (x*cos(x) + sin(x))*cos(x*sin(x))*log(sin(x))|
\ sin(x) /
$$x \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + \frac{\sin{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\sin{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)} + \sin^{\sin{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ / 2 2 \ \
sin(x*sin(x)) | | /cos(x)*sin(x*sin(x)) \ 2 cos (x)*sin(x*sin(x)) 2*(x*cos(x) + sin(x))*cos(x)*cos(x*sin(x)) | 2*cos(x)*sin(x*sin(x)) |
sin (x)*|- x*|- |-------------------- + (x*cos(x) + sin(x))*cos(x*sin(x))*log(sin(x))| + (x*cos(x) + sin(x)) *log(sin(x))*sin(x*sin(x)) + --------------------- + (-2*cos(x) + x*sin(x))*cos(x*sin(x))*log(sin(x)) - ------------------------------------------ + sin(x*sin(x))| + ---------------------- + 2*(x*cos(x) + sin(x))*cos(x*sin(x))*log(sin(x))|
| | \ sin(x) / 2 sin(x) | sin(x) |
\ \ sin (x) / /
$$\left(- x \left(\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \sin{\left(x \right)} \right)} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)} \cos{\left(x \sin{\left(x \right)} \right)}}{\sin{\left(x \right)}} - \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + \frac{\sin{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} + \sin{\left(x \sin{\left(x \right)} \right)} + \frac{\sin{\left(x \sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) + 2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + \frac{2 \sin{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\sin{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 2 / 3 / 2 \ 3 2 2 \ 2 \
sin(x*sin(x)) | /cos(x)*sin(x*sin(x)) \ | /cos(x)*sin(x*sin(x)) \ /cos(x)*sin(x*sin(x)) \ | 2 cos (x)*sin(x*sin(x)) 2*(x*cos(x) + sin(x))*cos(x)*cos(x*sin(x)) | 3 2*cos (x)*sin(x*sin(x)) 2*cos(x)*sin(x*sin(x)) 3*(x*cos(x) + sin(x)) *cos(x)*sin(x*sin(x)) 3*cos (x)*(x*cos(x) + sin(x))*cos(x*sin(x)) 3*(-2*cos(x) + x*sin(x))*cos(x)*cos(x*sin(x))| 2 3*cos (x)*sin(x*sin(x)) 6*(x*cos(x) + sin(x))*cos(x)*cos(x*sin(x))|
-sin (x)*|- 3*|-------------------- + (x*cos(x) + sin(x))*cos(x*sin(x))*log(sin(x))| + 3*sin(x*sin(x)) + x*|- |-------------------- + (x*cos(x) + sin(x))*cos(x*sin(x))*log(sin(x))| + 3*(x*cos(x) + sin(x))*cos(x*sin(x)) + 3*|-------------------- + (x*cos(x) + sin(x))*cos(x*sin(x))*log(sin(x))|*|(x*cos(x) + sin(x)) *log(sin(x))*sin(x*sin(x)) + --------------------- + (-2*cos(x) + x*sin(x))*cos(x*sin(x))*log(sin(x)) - ------------------------------------------ + sin(x*sin(x))| + (x*cos(x) + sin(x)) *cos(x*sin(x))*log(sin(x)) + (3*sin(x) + x*cos(x))*cos(x*sin(x))*log(sin(x)) - ----------------------- - ---------------------- - 3*(-2*cos(x) + x*sin(x))*(x*cos(x) + sin(x))*log(sin(x))*sin(x*sin(x)) + ------------------------------------------- + ------------------------------------------- + ---------------------------------------------| + 3*(x*cos(x) + sin(x)) *log(sin(x))*sin(x*sin(x)) + ----------------------- + 3*(-2*cos(x) + x*sin(x))*cos(x*sin(x))*log(sin(x)) - ------------------------------------------|
| \ sin(x) / | \ sin(x) / \ sin(x) / | 2 sin(x) | 3 sin(x) sin(x) 2 sin(x) | 2 sin(x) |
\ \ \ sin (x) / sin (x) sin (x) / sin (x) /
$$- \left(x \left(- 3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \sin{\left(x \right)} \right)} + \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(x \right)} \cos{\left(x \sin{\left(x \right)} \right)}}{\sin{\left(x \right)}} + \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{3} \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \sin{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + 3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \sin{\left(x \right)} \right)} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos^{2}{\left(x \right)} \cos{\left(x \sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} + \left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} - \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + \frac{\sin{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} + 3 \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + \frac{\sin{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \sin{\left(x \right)} \right)} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)} \cos{\left(x \sin{\left(x \right)} \right)}}{\sin{\left(x \right)}} + \sin{\left(x \sin{\left(x \right)} \right)} + \frac{\sin{\left(x \sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) - \frac{2 \sin{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{2 \sin{\left(x \sin{\left(x \right)} \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) + 3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + 3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \sin{\left(x \right)} \right)} - \frac{6 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)} \cos{\left(x \sin{\left(x \right)} \right)}}{\sin{\left(x \right)}} - 3 \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \sin{\left(x \right)} \right)} + \frac{\sin{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} + 3 \sin{\left(x \sin{\left(x \right)} \right)} + \frac{3 \sin{\left(x \sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{\sin{\left(x \sin{\left(x \right)} \right)}}{\left(x \right)}$$
Gráfico