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Derivada de:
Derivada de 8
Derivada de x^12
Derivada de (x+3)/(x-2)
Derivada de x*e^(1/x)
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
arctg(cos(x))
arctg(x+cosx)
arctg^3*4x*3^sinx
arctg^2(1/x)
Seno sin
sin^3x
sin(x/5)
sin(8*x)
sin(x-(3/5))-(8/5)
sin(v)
Coseno cos
cos(x)^(25)
cos2
cosx/lnx
cos(5-3*x)
cos(5*x)^(3)

Derivada de la función/ arctg/ cos(3x)/ sin(2x)/ y=arctg^3(sin(2x)*cos(3x))

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

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}

Simplificar

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}

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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}

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Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

Derivada de y=arctg^3(sin(2x)*cos(3x))

Gráfico:

Definida a trozos:

Solución