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y=arctg^21/2
Derivada de la función/ ctg^2/ arctg/ y=arctg^21/2

Derivada de y=arctg^21/2

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

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Solución

Ha introducido [src] 
    21/2   
atan    (x)
atan⁡212(x)\operatorname{atan}^{\frac{21}{2}}{\left(x \right)} 
atan(x)^(21/2)
Gráfica
02468-8-6-4-2-10100100
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Trazar el gráfico f'(x)
Primera derivada [src] 
       19/2   
21*atan    (x)
--------------
    /     2\  
  2*\1 + x /
21atan⁡192(x)2(x2+1)\frac{21 \operatorname{atan}^{\frac{19}{2}}{\left(x \right)}}{2 \left(x^{2} + 1\right)}
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Segunda derivada [src] 
       17/2                      
21*atan    (x)*(19/4 - x*atan(x))
---------------------------------
                    2            
            /     2\             
            \1 + x /
21(−xatan⁡(x)+194)atan⁡172(x)(x2+1)2\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}}
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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 /
21(4x2atan⁡2(x)x2+1−57xatan⁡(x)2(x2+1)−atan⁡2(x)+3238(x2+1))atan⁡152(x)(x2+1)2\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}}
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Gráfico
Derivada de y=arctg^21/2
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