Sr Examen

Derivada de y=tgx+arctgx

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

Gráfico:

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Solución

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