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Derivada de la función/ ctg2x/ arctg/ y=(arctg2x)^since

Derivada de y=(arctg2x)^since

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    sinc(E)     
atan       (2*x)
atan⁡sinc⁡(e)(2x)\operatorname{atan}^{\operatorname{sinc}{\left(e \right)}}{\left(2 x \right)} 
atan(2*x)^sinc(E)
Primera derivada [src] 
      sinc(E)             
2*atan       (2*x)*sinc(E)
--------------------------
   /       2\             
   \1 + 4*x /*atan(2*x)
2atan⁡sinc⁡(e)(2x)sinc⁡(e)(4x2+1)atan⁡(2x)\frac{2 \operatorname{atan}^{\operatorname{sinc}{\left(e \right)}}{\left(2 x \right)} \operatorname{sinc}{\left(e \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}
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Segunda derivada [src] 
      sinc(E)      /      1              sinc(E) \        
4*atan       (2*x)*|- --------- - 4*x + ---------|*sinc(E)
                   \  atan(2*x)         atan(2*x)/        
----------------------------------------------------------
                            2                             
                  /       2\                              
                  \1 + 4*x / *atan(2*x)
4(−4x−1atan⁡(2x)+sinc⁡(e)atan⁡(2x))atan⁡sinc⁡(e)(2x)sinc⁡(e)(4x2+1)2atan⁡(2x)\frac{4 \left(- 4 x - \frac{1}{\operatorname{atan}{\left(2 x \right)}} + \frac{\operatorname{sinc}{\left(e \right)}}{\operatorname{atan}{\left(2 x \right)}}\right) \operatorname{atan}^{\operatorname{sinc}{\left(e \right)}}{\left(2 x \right)} \operatorname{sinc}{\left(e \right)}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}}
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Tercera derivada [src] 
                   /                                  2                2                                                                               \        
      sinc(E)      |               2              32*x             sinc (E)               3*sinc(E)                 12*x               12*x*sinc(E)    |        
8*atan       (2*x)*|-2 + --------------------- + -------- + --------------------- - --------------------- + -------------------- - --------------------|*sinc(E)
                   |     /       2\     2               2   /       2\     2        /       2\     2        /       2\             /       2\          |        
                   \     \1 + 4*x /*atan (2*x)   1 + 4*x    \1 + 4*x /*atan (2*x)   \1 + 4*x /*atan (2*x)   \1 + 4*x /*atan(2*x)   \1 + 4*x /*atan(2*x)/        
----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                               2                                                                                
                                                                     /       2\                                                                                 
                                                                     \1 + 4*x / *atan(2*x)
8(32x24x2+1−12xsinc⁡(e)(4x2+1)atan⁡(2x)+12x(4x2+1)atan⁡(2x)−2−3sinc⁡(e)(4x2+1)atan⁡2(2x)+sinc⁡2(e)(4x2+1)atan⁡2(2x)+2(4x2+1)atan⁡2(2x))atan⁡sinc⁡(e)(2x)sinc⁡(e)(4x2+1)2atan⁡(2x)\frac{8 \left(\frac{32 x^{2}}{4 x^{2} + 1} - \frac{12 x \operatorname{sinc}{\left(e \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{12 x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - 2 - \frac{3 \operatorname{sinc}{\left(e \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)}} + \frac{\operatorname{sinc}^{2}{\left(e \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)}} + \frac{2}{\left(4 x^{2} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)}}\right) \operatorname{atan}^{\operatorname{sinc}{\left(e \right)}}{\left(2 x \right)} \operatorname{sinc}{\left(e \right)}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}}
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