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(x+(x^(2)+1)*atan(x))/2*(x^(2)+1)

Derivada de (x+(x^(2)+1)*atan(x))/2*(x^(2)+1)

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

Gráfico:

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Solución

Ha introducido [src]
    / 2    \                 
x + \x  + 1/*atan(x) / 2    \
--------------------*\x  + 1/
         2                   
$$\frac{x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{2} \left(x^{2} + 1\right)$$
((x + (x^2 + 1)*atan(x))/2)*(x^2 + 1)
Gráfica
Primera derivada [src]
                                    /                   2      \
  /    / 2    \        \   / 2    \ |1                 x  + 1  |
x*\x + \x  + 1/*atan(x)/ + \x  + 1/*|- + x*atan(x) + ----------|
                                    |2                 /     2\|
                                    \                2*\1 + x //
$$x \left(x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}\right) + \left(x^{2} + 1\right) \left(x \operatorname{atan}{\left(x \right)} + \frac{x^{2} + 1}{2 \left(x^{2} + 1\right)} + \frac{1}{2}\right)$$
Segunda derivada [src]
    /     2\ /  x             \   /     2\                              
x + \1 + x /*|------ + atan(x)| + \1 + x /*atan(x) + 4*x*(1 + x*atan(x))
             |     2          |                                         
             \1 + x           /                                         
$$4 x \left(x \operatorname{atan}{\left(x \right)} + 1\right) + x + \left(x^{2} + 1\right) \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}$$
Tercera derivada [src]
  /       2                                         \
  |      x          /  x             \              |
2*|4 - ------ + 3*x*|------ + atan(x)| + 3*x*atan(x)|
  |         2       |     2          |              |
  \    1 + x        \1 + x           /              /
$$2 \left(- \frac{x^{2}}{x^{2} + 1} + 3 x \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) + 3 x \operatorname{atan}{\left(x \right)} + 4\right)$$
Gráfico
Derivada de (x+(x^(2)+1)*atan(x))/2*(x^(2)+1)