Sr Examen

Otras calculadoras


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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
    2    /  ___      2\
atan (x)*\\/ x  + 3*x /
$$\left(\sqrt{x} + 3 x^{2}\right) \operatorname{atan}^{2}{\left(x \right)}$$
atan(x)^2*(sqrt(x) + 3*x^2)
Gráfica
Primera derivada [src]
                             /  ___      2\        
    2    /   1         \   2*\\/ x  + 3*x /*atan(x)
atan (x)*|------- + 6*x| + ------------------------
         |    ___      |                 2         
         \2*\/ x       /            1 + x          
$$\frac{2 \left(\sqrt{x} + 3 x^{2}\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \left(6 x + \frac{1}{2 \sqrt{x}}\right) \operatorname{atan}^{2}{\left(x \right)}$$
Segunda derivada [src]
    2    /      1  \                                           /  1         \        
atan (x)*|24 - ----|                                         2*|----- + 12*x|*atan(x)
         |      3/2|                        /  ___      2\     |  ___       |        
         \     x   /   2*(-1 + 2*x*atan(x))*\\/ x  + 3*x /     \\/ x        /        
-------------------- - ----------------------------------- + ------------------------
         4                                  2                              2         
                                    /     2\                          1 + x          
                                    \1 + x /                                         
$$\frac{\left(24 - \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{atan}^{2}{\left(x \right)}}{4} - \frac{2 \left(\sqrt{x} + 3 x^{2}\right) \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(12 x + \frac{1}{\sqrt{x}}\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
Tercera derivada [src]
                              /            2                  \                                                              
               /  ___      2\ | 3*x     4*x *atan(x)          |                        /  1         \     /      1  \        
             4*\\/ x  + 3*x /*|------ - ------------ + atan(x)|   3*(-1 + 2*x*atan(x))*|----- + 12*x|   3*|24 - ----|*atan(x)
      2                       |     2           2             |                        |  ___       |     |      3/2|        
3*atan (x)                    \1 + x       1 + x              /                        \\/ x        /     \     x   /        
---------- - -------------------------------------------------- - ----------------------------------- + ---------------------
     5/2                                 2                                             2                        /     2\     
  8*x                            /     2\                                      /     2\                       2*\1 + x /     
                                 \1 + x /                                      \1 + x /                                      
$$\frac{3 \left(24 - \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{atan}{\left(x \right)}}{2 \left(x^{2} + 1\right)} - \frac{4 \left(\sqrt{x} + 3 x^{2}\right) \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(12 x + \frac{1}{\sqrt{x}}\right) \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{8 x^{\frac{5}{2}}}$$
Gráfico
Derivada de y=(arctg^2)(sqrtx+3x^2)