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 -2x
-
Derivada de 1/x^5
-
Derivada de e^-1
-
Derivada de x^2sinx
-
Expresiones idénticas
- y=arctg^ tres (sin(2x)*cos(3x))
- y es igual a arctg al cubo ( seno de (2x) multiplicar por coseno de (3x))
- y es igual a arctg en el grado tres ( seno de (2x) multiplicar por coseno de (3x))
- y=arctg3(sin(2x)*cos(3x))
- y=arctg3sin2x*cos3x
- y=arctg³(sin(2x)*cos(3x))
- y=arctg en el grado 3(sin(2x)*cos(3x))
- y=arctg^3(sin(2x)cos(3x))
- y=arctg3(sin(2x)cos(3x))
- y=arctg3sin2xcos3x
- y=arctg^3sin2xcos3x
-
Expresiones con funciones
- arctg
- arctg3
- arctg(sqrt(x))
- arctg(cos(x))
- arctg^2(1/x)
- arctg(x+cosx)
- Seno sin
- sin^3*x
- sin(5-3*x)
- sin(x/5)
- sin²(x)
- sin(x)/3
- Coseno cos
- cos(3)^(2)*x
- cos^2(x^2)
- cos/sin
- cosx-sinx
- cosx^(sinx)
Derivada de y=arctg^3(sin(2x)*cos(3x))
Solución
Ha introducido
[src]
3 atan (sin(2*x)*cos(3*x))
$$\operatorname{atan}^{3}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}$$
atan(sin(2*x)*cos(3*x))^3
Primera derivada
[src]
2
3*atan (sin(2*x)*cos(3*x))*(-3*sin(2*x)*sin(3*x) + 2*cos(2*x)*cos(3*x))
-----------------------------------------------------------------------
2 2
1 + cos (3*x)*sin (2*x)
$$\frac{3 \left(- 3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} + 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right) \operatorname{atan}^{2}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1}$$
Segunda derivada
[src]
/ 2 2 \
| 2*(-2*cos(2*x)*cos(3*x) + 3*sin(2*x)*sin(3*x)) 2*(-2*cos(2*x)*cos(3*x) + 3*sin(2*x)*sin(3*x)) *atan(cos(3*x)*sin(2*x))*cos(3*x)*sin(2*x)|
3*|-(12*cos(2*x)*sin(3*x) + 13*cos(3*x)*sin(2*x))*atan(cos(3*x)*sin(2*x)) + ----------------------------------------------- - -----------------------------------------------------------------------------------------|*atan(cos(3*x)*sin(2*x))
| 2 2 2 2 |
\ 1 + cos (3*x)*sin (2*x) 1 + cos (3*x)*sin (2*x) /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
1 + cos (3*x)*sin (2*x)
$$\frac{3 \left(- \frac{2 \left(3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right)^{2} \sin{\left(2 x \right)} \cos{\left(3 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1} + \frac{2 \left(3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right)^{2}}{\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1} - \left(13 \sin{\left(2 x \right)} \cos{\left(3 x \right)} + 12 \sin{\left(3 x \right)} \cos{\left(2 x \right)}\right) \operatorname{atan}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}\right) \operatorname{atan}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1}$$
Tercera derivada
[src]
/ 3 2 / 2 2 2 2 2 2 \ 3 2 2 2 3 2 \
| 2 2*(-2*cos(2*x)*cos(3*x) + 3*sin(2*x)*sin(3*x)) 2*atan (cos(3*x)*sin(2*x))*(-2*cos(2*x)*cos(3*x) + 3*sin(2*x)*sin(3*x))*\- 13*cos (3*x)*sin (2*x) + 4*cos (2*x)*cos (3*x) + 9*sin (2*x)*sin (3*x) - 24*cos(2*x)*cos(3*x)*sin(2*x)*sin(3*x)/ 6*(-2*cos(2*x)*cos(3*x) + 3*sin(2*x)*sin(3*x))*(12*cos(2*x)*sin(3*x) + 13*cos(3*x)*sin(2*x))*atan(cos(3*x)*sin(2*x)) 8*(-2*cos(2*x)*cos(3*x) + 3*sin(2*x)*sin(3*x)) *atan (cos(3*x)*sin(2*x))*cos (3*x)*sin (2*x) 12*(-2*cos(2*x)*cos(3*x) + 3*sin(2*x)*sin(3*x)) *atan(cos(3*x)*sin(2*x))*cos(3*x)*sin(2*x) 4*atan (cos(3*x)*sin(2*x))*(-2*cos(2*x)*cos(3*x) + 3*sin(2*x)*sin(3*x))*(12*cos(2*x)*sin(3*x) + 13*cos(3*x)*sin(2*x))*cos(3*x)*sin(2*x)|
3*|atan (cos(3*x)*sin(2*x))*(-62*cos(2*x)*cos(3*x) + 63*sin(2*x)*sin(3*x)) - ----------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------|
| 2 2 2 2 2 2 2 2 2 |
| / 2 2 \ 1 + cos (3*x)*sin (2*x) 1 + cos (3*x)*sin (2*x) / 2 2 \ / 2 2 \ 1 + cos (3*x)*sin (2*x) |
\ \1 + cos (3*x)*sin (2*x)/ \1 + cos (3*x)*sin (2*x)/ \1 + cos (3*x)*sin (2*x)/ /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
1 + cos (3*x)*sin (2*x)
$$\frac{3 \left(- \frac{8 \left(3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right)^{3} \sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} \operatorname{atan}^{2}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}}{\left(\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1\right)^{2}} + \frac{12 \left(3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right)^{3} \sin{\left(2 x \right)} \cos{\left(3 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}}{\left(\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1\right)^{2}} - \frac{2 \left(3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right)^{3}}{\left(\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1\right)^{2}} - \frac{4 \left(3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right) \left(13 \sin{\left(2 x \right)} \cos{\left(3 x \right)} + 12 \sin{\left(3 x \right)} \cos{\left(2 x \right)}\right) \sin{\left(2 x \right)} \cos{\left(3 x \right)} \operatorname{atan}^{2}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1} + \frac{6 \left(3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right) \left(13 \sin{\left(2 x \right)} \cos{\left(3 x \right)} + 12 \sin{\left(3 x \right)} \cos{\left(2 x \right)}\right) \operatorname{atan}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1} + \frac{2 \left(3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right) \left(9 \sin^{2}{\left(2 x \right)} \sin^{2}{\left(3 x \right)} - 13 \sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} - 24 \sin{\left(2 x \right)} \sin{\left(3 x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)} + 4 \cos^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)}\right) \operatorname{atan}^{2}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1} + \left(63 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 62 \cos{\left(2 x \right)} \cos{\left(3 x \right)}\right) \operatorname{atan}^{2}{\left(\sin{\left(2 x \right)} \cos{\left(3 x \right)} \right)}\right)}{\sin^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)} + 1}$$
Gráfico