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)/x^2
-
Derivada de 2/x²
-
Derivada de -2*y
-
Derivada de 3/2x
-
Expresiones idénticas
- y=arctg^(tres)x-3sinx^(dos)
- y es igual a arctg en el grado (3)x menos 3 seno de x en el grado (2)
- y es igual a arctg en el grado (tres)x menos 3 seno de x en el grado (dos)
- y=arctg(3)x-3sinx(2)
- y=arctg3x-3sinx2
- y=arctg^3x-3sinx^2
-
Expresiones semejantes
- y=arctg^(3)x+3sinx^(2)
Derivada de y=arctg^(3)x-3sinx^(2)
Solución
Ha introducido
[src]
3 2 atan (x - 3*sin(x))*x
$$x^{2} \operatorname{atan}^{3}{\left(x - 3 \sin{\left(x \right)} \right)}$$
atan(x - 3*sin(x))^3*x^2
Primera derivada
[src]
2 2
3 3*x *atan (x - 3*sin(x))*(1 - 3*cos(x))
2*x*atan (x - 3*sin(x)) + ---------------------------------------
2
1 + (x - 3*sin(x))
$$\frac{3 x^{2} \left(1 - 3 \cos{\left(x \right)}\right) \operatorname{atan}^{2}{\left(x - 3 \sin{\left(x \right)} \right)}}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1} + 2 x \operatorname{atan}^{3}{\left(x - 3 \sin{\left(x \right)} \right)}$$
Segunda derivada
[src]
/ / 2 2 \ \ | 2 | 2*(-1 + 3*cos(x)) 2*(-1 + 3*cos(x)) *(x - 3*sin(x))*atan(x - 3*sin(x))| | | 3*x *|------------------- + 3*atan(x - 3*sin(x))*sin(x) - ----------------------------------------------------| | | | 2 2 | | | 2 \1 + (x - 3*sin(x)) 1 + (x - 3*sin(x)) / 12*x*(-1 + 3*cos(x))*atan(x - 3*sin(x))| |2*atan (x - 3*sin(x)) + --------------------------------------------------------------------------------------------------------------- - ---------------------------------------|*atan(x - 3*sin(x)) | 2 2 | \ 1 + (x - 3*sin(x)) 1 + (x - 3*sin(x)) /
$$\left(\frac{3 x^{2} \left(- \frac{2 \left(x - 3 \sin{\left(x \right)}\right) \left(3 \cos{\left(x \right)} - 1\right)^{2} \operatorname{atan}{\left(x - 3 \sin{\left(x \right)} \right)}}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1} + 3 \sin{\left(x \right)} \operatorname{atan}{\left(x - 3 \sin{\left(x \right)} \right)} + \frac{2 \left(3 \cos{\left(x \right)} - 1\right)^{2}}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1}\right)}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1} - \frac{12 x \left(3 \cos{\left(x \right)} - 1\right) \operatorname{atan}{\left(x - 3 \sin{\left(x \right)} \right)}}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1} + 2 \operatorname{atan}^{2}{\left(x - 3 \sin{\left(x \right)} \right)}\right) \operatorname{atan}{\left(x - 3 \sin{\left(x \right)} \right)}$$
Tercera derivada
[src]
/ / 3 3 2 3 2 2 3 2 \ / 2 2 \ \
| 2 | 2*(-1 + 3*cos(x)) 2 2*(-1 + 3*cos(x)) *atan (x - 3*sin(x)) 18*(-1 + 3*cos(x))*atan(x - 3*sin(x))*sin(x) 8*(-1 + 3*cos(x)) *(x - 3*sin(x)) *atan (x - 3*sin(x)) 12*(-1 + 3*cos(x)) *(x - 3*sin(x))*atan(x - 3*sin(x)) 18*atan (x - 3*sin(x))*(-1 + 3*cos(x))*(x - 3*sin(x))*sin(x)| 2 | 2*(-1 + 3*cos(x)) 2*(-1 + 3*cos(x)) *(x - 3*sin(x))*atan(x - 3*sin(x))| |
3*|x *|- ---------------------- + 3*atan (x - 3*sin(x))*cos(x) + -------------------------------------- - -------------------------------------------- - ------------------------------------------------------ + ----------------------------------------------------- + ------------------------------------------------------------| - 6*atan (x - 3*sin(x))*(-1 + 3*cos(x)) + 6*x*|------------------- + 3*atan(x - 3*sin(x))*sin(x) - ----------------------------------------------------|*atan(x - 3*sin(x))|
| | 2 2 2 2 2 2 | | 2 2 | |
| | / 2\ 1 + (x - 3*sin(x)) 1 + (x - 3*sin(x)) / 2\ / 2\ 1 + (x - 3*sin(x)) | \1 + (x - 3*sin(x)) 1 + (x - 3*sin(x)) / |
\ \ \1 + (x - 3*sin(x)) / \1 + (x - 3*sin(x)) / \1 + (x - 3*sin(x)) / / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
1 + (x - 3*sin(x))
$$\frac{3 \left(x^{2} \left(- \frac{8 \left(x - 3 \sin{\left(x \right)}\right)^{2} \left(3 \cos{\left(x \right)} - 1\right)^{3} \operatorname{atan}^{2}{\left(x - 3 \sin{\left(x \right)} \right)}}{\left(\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1\right)^{2}} + \frac{18 \left(x - 3 \sin{\left(x \right)}\right) \left(3 \cos{\left(x \right)} - 1\right) \sin{\left(x \right)} \operatorname{atan}^{2}{\left(x - 3 \sin{\left(x \right)} \right)}}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1} + \frac{12 \left(x - 3 \sin{\left(x \right)}\right) \left(3 \cos{\left(x \right)} - 1\right)^{3} \operatorname{atan}{\left(x - 3 \sin{\left(x \right)} \right)}}{\left(\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1\right)^{2}} + 3 \cos{\left(x \right)} \operatorname{atan}^{2}{\left(x - 3 \sin{\left(x \right)} \right)} + \frac{2 \left(3 \cos{\left(x \right)} - 1\right)^{3} \operatorname{atan}^{2}{\left(x - 3 \sin{\left(x \right)} \right)}}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1} - \frac{18 \left(3 \cos{\left(x \right)} - 1\right) \sin{\left(x \right)} \operatorname{atan}{\left(x - 3 \sin{\left(x \right)} \right)}}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1} - \frac{2 \left(3 \cos{\left(x \right)} - 1\right)^{3}}{\left(\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1\right)^{2}}\right) + 6 x \left(- \frac{2 \left(x - 3 \sin{\left(x \right)}\right) \left(3 \cos{\left(x \right)} - 1\right)^{2} \operatorname{atan}{\left(x - 3 \sin{\left(x \right)} \right)}}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1} + 3 \sin{\left(x \right)} \operatorname{atan}{\left(x - 3 \sin{\left(x \right)} \right)} + \frac{2 \left(3 \cos{\left(x \right)} - 1\right)^{2}}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1}\right) \operatorname{atan}{\left(x - 3 \sin{\left(x \right)} \right)} - 6 \left(3 \cos{\left(x \right)} - 1\right) \operatorname{atan}^{2}{\left(x - 3 \sin{\left(x \right)} \right)}\right)}{\left(x - 3 \sin{\left(x \right)}\right)^{2} + 1}$$
Gráfico