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y=sin^43x*arctg2x^3
Derivada de la función/ ctg2x/ arctg/ sin^4/ y=sin/ y=sin^43x*arctg2x^3

Derivada de y=sin^43x*arctg2x^3

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   4          3     
sin (3*x)*atan (2*x)
sin⁡4(3x)atan⁡3(2x)\sin^{4}{\left(3 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} 
sin(3*x)^4*atan(2*x)^3
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      2         4                                        
6*atan (2*x)*sin (3*x)          3         3              
---------------------- + 12*atan (2*x)*sin (3*x)*cos(3*x)
              2                                          
       1 + 4*x
12sin⁡3(3x)cos⁡(3x)atan⁡3(2x)+6sin⁡4(3x)atan⁡2(2x)4x2+112 \sin^{3}{\left(3 x \right)} \cos{\left(3 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{6 \sin^{4}{\left(3 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1}
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Segunda derivada [src] 
             /                                                2                                                           \          
      2      |        2      /   2             2     \   2*sin (3*x)*(-1 + 2*x*atan(2*x))   12*atan(2*x)*cos(3*x)*sin(3*x)|          
12*sin (3*x)*|- 3*atan (2*x)*\sin (3*x) - 3*cos (3*x)/ - -------------------------------- + ------------------------------|*atan(2*x)
             |                                                               2                                2           |          
             |                                                     /       2\                          1 + 4*x            |          
             \                                                     \1 + 4*x /                                             /
12(−3(sin⁡2(3x)−3cos⁡2(3x))atan⁡2(2x)+12sin⁡(3x)cos⁡(3x)atan⁡(2x)4x2+1−2(2xatan⁡(2x)−1)sin⁡2(3x)(4x2+1)2)sin⁡2(3x)atan⁡(2x)12 \left(- 3 \left(\sin^{2}{\left(3 x \right)} - 3 \cos^{2}{\left(3 x \right)}\right) \operatorname{atan}^{2}{\left(2 x \right)} + \frac{12 \sin{\left(3 x \right)} \cos{\left(3 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{2 \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(3 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin^{2}{\left(3 x \right)} \operatorname{atan}{\left(2 x \right)}
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Tercera derivada [src] 
   /                                                                    /                                             2     2     \                                                                                                          \         
   |                                                             3      |   1           2        12*x*atan(2*x)   16*x *atan (2*x)|                                                                                                          |         
   |                                                        2*sin (3*x)*|-------- - atan (2*x) - -------------- + ----------------|                                                                                                          |         
   |                                                                    |       2                          2                 2    |          2      /   2             2     \                  2                                             |         
   |        3      /       2             2     \                        \1 + 4*x                    1 + 4*x           1 + 4*x     /   27*atan (2*x)*\sin (3*x) - 3*cos (3*x)/*sin(3*x)   36*sin (3*x)*(-1 + 2*x*atan(2*x))*atan(2*x)*cos(3*x)|         
24*|- 9*atan (2*x)*\- 3*cos (3*x) + 5*sin (3*x)/*cos(3*x) + ----------------------------------------------------------------------- - ------------------------------------------------ - ----------------------------------------------------|*sin(3*x)
   |                                                                                                2                                                            2                                                     2                     |         
   |                                                                                      /       2\                                                      1 + 4*x                                            /       2\                      |         
   \                                                                                      \1 + 4*x /                                                                                                         \1 + 4*x /                      /
24(−9(5sin⁡2(3x)−3cos⁡2(3x))cos⁡(3x)atan⁡3(2x)−27(sin⁡2(3x)−3cos⁡2(3x))sin⁡(3x)atan⁡2(2x)4x2+1−36(2xatan⁡(2x)−1)sin⁡2(3x)cos⁡(3x)atan⁡(2x)(4x2+1)2+2(16x2atan⁡2(2x)4x2+1−12xatan⁡(2x)4x2+1−atan⁡2(2x)+14x2+1)sin⁡3(3x)(4x2+1)2)sin⁡(3x)24 \left(- 9 \left(5 \sin^{2}{\left(3 x \right)} - 3 \cos^{2}{\left(3 x \right)}\right) \cos{\left(3 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} - \frac{27 \left(\sin^{2}{\left(3 x \right)} - 3 \cos^{2}{\left(3 x \right)}\right) \sin{\left(3 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{36 \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)} \operatorname{atan}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{2 \left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) \sin^{3}{\left(3 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin{\left(3 x \right)}
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Gráfico
Derivada de y=sin^43x*arctg2x^3
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