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(x+x^3)*arctg(x)

Derivada de (x+x^3)*arctg(x)

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

Ha introducido [src]
/     3\        
\x + x /*atan(x)
$$\left(x^{3} + x\right) \operatorname{atan}{\left(x \right)}$$
(x + x^3)*atan(x)
Gráfica
Primera derivada [src]
     3                     
x + x    /       2\        
------ + \1 + 3*x /*atan(x)
     2                     
1 + x                      
$$\left(3 x^{2} + 1\right) \operatorname{atan}{\left(x \right)} + \frac{x^{3} + x}{x^{2} + 1}$$
Segunda derivada [src]
  /       2      2                \
  |1 + 3*x      x                 |
2*|-------- - ------ + 3*x*atan(x)|
  |      2         2              |
  \ 1 + x     1 + x               /
$$2 \left(- \frac{x^{2}}{x^{2} + 1} + 3 x \operatorname{atan}{\left(x \right)} + \frac{3 x^{2} + 1}{x^{2} + 1}\right)$$
Tercera derivada [src]
  /                       /         2 \                 \
  |                       |      4*x  |                 |
  |                     x*|-1 + ------|                 |
  |                       |          2|       /       2\|
  |             9*x       \     1 + x /   3*x*\1 + 3*x /|
2*|3*atan(x) + ------ + --------------- - --------------|
  |                 2             2                 2   |
  |            1 + x         1 + x          /     2\    |
  \                                         \1 + x /    /
$$2 \left(\frac{x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + \frac{9 x}{x^{2} + 1} - \frac{3 x \left(3 x^{2} + 1\right)}{\left(x^{2} + 1\right)^{2}} + 3 \operatorname{atan}{\left(x \right)}\right)$$
Gráfico
Derivada de (x+x^3)*arctg(x)