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y=(arctg^2)sqrtx+3x^2

Derivada de y=(arctg^2)sqrtx+3x^2

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

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Solución

Ha introducido [src]
    2      ___      2
atan (x)*\/ x  + 3*x 
$$\sqrt{x} \operatorname{atan}^{2}{\left(x \right)} + 3 x^{2}$$
atan(x)^2*sqrt(x) + 3*x^2
Gráfica
Primera derivada [src]
          2          ___        
      atan (x)   2*\/ x *atan(x)
6*x + -------- + ---------------
          ___              2    
      2*\/ x          1 + x     
$$\frac{2 \sqrt{x} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + 6 x + \frac{\operatorname{atan}^{2}{\left(x \right)}}{2 \sqrt{x}}$$
Segunda derivada [src]
         ___        2         3/2                         
     2*\/ x     atan (x)   4*x   *atan(x)     2*atan(x)   
6 + --------- - -------- - -------------- + --------------
            2       3/2              2        ___ /     2\
    /     2\     4*x         /     2\       \/ x *\1 + x /
    \1 + x /                 \1 + x /                     
$$- \frac{4 x^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \sqrt{x}}{\left(x^{2} + 1\right)^{2}} + 6 + \frac{2 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{4 x^{\frac{3}{2}}}$$
Tercera derivada [src]
       3/2                            2           ___               5/2                          
   12*x              3          3*atan (x)   10*\/ x *atan(x)   16*x   *atan(x)      3*atan(x)   
- --------- + --------------- + ---------- - ---------------- + --------------- - ---------------
          3                 2        5/2                2                  3         3/2 /     2\
  /     2\      ___ /     2\      8*x           /     2\           /     2\       2*x   *\1 + x /
  \1 + x /    \/ x *\1 + x /                    \1 + x /           \1 + x /                      
$$\frac{16 x^{\frac{5}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x^{\frac{3}{2}}}{\left(x^{2} + 1\right)^{3}} - \frac{10 \sqrt{x} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{3 \operatorname{atan}{\left(x \right)}}{2 x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{8 x^{\frac{5}{2}}}$$
Gráfico
Derivada de y=(arctg^2)sqrtx+3x^2