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y=1/x+3/arctg(x)-arctg3(x)/2+e^2

Derivada de y=1/x+3/arctg(x)-arctg3(x)/2+e^2

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

Gráfico:

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Solución

Ha introducido [src]
1      3      atan(3)*x    2
- + ------- - --------- + E 
x   atan(x)       2         
$$\left(- \frac{x \operatorname{atan}{\left(3 \right)}}{2} + \left(\frac{3}{\operatorname{atan}{\left(x \right)}} + \frac{1}{x}\right)\right) + e^{2}$$
1/x + 3/atan(x) - atan(3)*x/2 + E^2
Gráfica
Primera derivada [src]
  1    atan(3)           3        
- -- - ------- - -----------------
   2      2      /     2\     2   
  x              \1 + x /*atan (x)
$$- \frac{\operatorname{atan}{\left(3 \right)}}{2} - \frac{3}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}} - \frac{1}{x^{2}}$$
Segunda derivada [src]
  /1            3                   3*x        \
2*|-- + ------------------ + ------------------|
  | 3           2                    2         |
  |x    /     2\      3      /     2\      2   |
  \     \1 + x / *atan (x)   \1 + x / *atan (x)/
$$2 \left(\frac{3 x}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} + \frac{3}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{3}{\left(x \right)}} + \frac{1}{x^{3}}\right)$$
Tercera derivada [src]
  /                                                                                2       \
  |  1            1                    3                   6*x                  4*x        |
6*|- -- + ------------------ - ------------------ - ------------------ - ------------------|
  |   4           2                    3                    3                    3         |
  |  x    /     2\      2      /     2\      4      /     2\      3      /     2\      2   |
  \       \1 + x / *atan (x)   \1 + x / *atan (x)   \1 + x / *atan (x)   \1 + x / *atan (x)/
$$6 \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(x \right)}} - \frac{6 x}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(x \right)}} + \frac{1}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} - \frac{3}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{4}{\left(x \right)}} - \frac{1}{x^{4}}\right)$$
Gráfico
Derivada de y=1/x+3/arctg(x)-arctg3(x)/2+e^2