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Derivada de xtgx+4arccosx

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

Gráfico:

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Solución

Ha introducido [src]
x*tan(x) + 4*acos(x)
$$x \tan{\left(x \right)} + 4 \operatorname{acos}{\left(x \right)}$$
x*tan(x) + 4*acos(x)
Gráfica
Primera derivada [src]
       4          /       2   \         
- ----------- + x*\1 + tan (x)/ + tan(x)
     ________                           
    /      2                            
  \/  1 - x                             
$$x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)} - \frac{4}{\sqrt{1 - x^{2}}}$$
Segunda derivada [src]
  /       2          2*x         /       2   \       \
2*|1 + tan (x) - ----------- + x*\1 + tan (x)/*tan(x)|
  |                      3/2                         |
  |              /     2\                            |
  \              \1 - x /                            /
$$2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{2 x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \tan^{2}{\left(x \right)} + 1\right)$$
Tercera derivada [src]
  /                               2          2                                                        \
  |       2          /       2   \        6*x         /       2   \                 2    /       2   \|
2*|- ----------- + x*\1 + tan (x)/  - ----------- + 3*\1 + tan (x)/*tan(x) + 2*x*tan (x)*\1 + tan (x)/|
  |          3/2                              5/2                                                     |
  |  /     2\                         /     2\                                                        |
  \  \1 - x /                         \1 - x /                                                        /
$$2 \left(- \frac{6 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{2}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)$$
Gráfico
Derivada de xtgx+4arccosx