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y=arctg^21/2

Derivada de y=arctg^21/2

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

Gráfico:

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Solución

Ha introducido [src]
    21/2   
atan    (x)
$$\operatorname{atan}^{\frac{21}{2}}{\left(x \right)}$$
atan(x)^(21/2)
Gráfica
Primera derivada [src]
       19/2   
21*atan    (x)
--------------
    /     2\  
  2*\1 + x /  
$$\frac{21 \operatorname{atan}^{\frac{19}{2}}{\left(x \right)}}{2 \left(x^{2} + 1\right)}$$
Segunda derivada [src]
       17/2                      
21*atan    (x)*(19/4 - x*atan(x))
---------------------------------
                    2            
            /     2\             
            \1 + x /             
$$\frac{21 \left(- x \operatorname{atan}{\left(x \right)} + \frac{19}{4}\right) \operatorname{atan}^{\frac{17}{2}}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}$$
Tercera derivada [src]
               /                             2     2                  \
       15/2    |      2         323       4*x *atan (x)   57*x*atan(x)|
21*atan    (x)*|- atan (x) + ---------- + ------------- - ------------|
               |               /     2\            2         /     2\ |
               \             8*\1 + x /       1 + x        2*\1 + x / /
-----------------------------------------------------------------------
                                       2                               
                               /     2\                                
                               \1 + x /                                
$$\frac{21 \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{57 x \operatorname{atan}{\left(x \right)}}{2 \left(x^{2} + 1\right)} - \operatorname{atan}^{2}{\left(x \right)} + \frac{323}{8 \left(x^{2} + 1\right)}\right) \operatorname{atan}^{\frac{15}{2}}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}$$
Gráfico
Derivada de y=arctg^21/2