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y=tg^3(x)·arctg(x)

Derivada de y=tg^3(x)·arctg(x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
   3           
tan (x)*atan(x)
$$\tan^{3}{\left(x \right)} \operatorname{atan}{\left(x \right)}$$
tan(x)^3*atan(x)
Gráfica
Primera derivada [src]
   3                                     
tan (x)      2    /         2   \        
------- + tan (x)*\3 + 3*tan (x)/*atan(x)
      2                                  
 1 + x                                   
$$\left(3 \tan^{2}{\left(x \right)} + 3\right) \tan^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{\tan^{3}{\left(x \right)}}{x^{2} + 1}$$
Segunda derivada [src]
  /       2        /       2   \                                                 \       
  |  x*tan (x)   3*\1 + tan (x)/*tan(x)     /       2   \ /         2   \        |       
2*|- --------- + ---------------------- + 3*\1 + tan (x)/*\1 + 2*tan (x)/*atan(x)|*tan(x)
  |          2                2                                                  |       
  |  /     2\            1 + x                                                   |       
  \  \1 + x /                                                                    /       
$$2 \left(- \frac{x \tan^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + 3 \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 \tan^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2} + 1}\right) \tan{\left(x \right)}$$
Tercera derivada [src]
  /        /         2 \                                                                                                                                                      \
  |   3    |      4*x  |                                                                                                                                                      |
  |tan (x)*|-1 + ------|                                                                                                                                                      |
  |        |          2|                   /             2                                      \                  2    /       2   \     /       2   \ /         2   \       |
  |        \     1 + x /     /       2   \ |/       2   \         4           2    /       2   \|           9*x*tan (x)*\1 + tan (x)/   9*\1 + tan (x)/*\1 + 2*tan (x)/*tan(x)|
2*|--------------------- + 3*\1 + tan (x)/*\\1 + tan (x)/  + 2*tan (x) + 7*tan (x)*\1 + tan (x)//*atan(x) - ------------------------- + --------------------------------------|
  |              2                                                                                                          2                                2                |
  |      /     2\                                                                                                   /     2\                            1 + x                 |
  \      \1 + x /                                                                                                   \1 + x /                                                  /
$$2 \left(- \frac{9 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + 3 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 7 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 2 \tan^{4}{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{9 \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 \tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2} + 1} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \tan^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)$$
Gráfico
Derivada de y=tg^3(x)·arctg(x)