Sr Examen

Derivada de (π-2arctgx)lnx

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

Gráfico:

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Solución

Ha introducido [src]
(pi - 2*acot(x))*log(x)
$$\left(\pi - 2 \operatorname{acot}{\left(x \right)}\right) \log{\left(x \right)}$$
(pi - 2*acot(x))*log(x)
Gráfica
Primera derivada [src]
pi - 2*acot(x)   2*log(x)
-------------- + --------
      x                2 
                  1 + x  
$$\frac{2 \log{\left(x \right)}}{x^{2} + 1} + \frac{\pi - 2 \operatorname{acot}{\left(x \right)}}{x}$$
Segunda derivada [src]
-pi + 2*acot(x)       4        4*x*log(x)
--------------- + ---------- - ----------
        2           /     2\           2 
       x          x*\1 + x /   /     2\  
                               \1 + x /  
$$- \frac{4 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{4}{x \left(x^{2} + 1\right)} + \frac{2 \operatorname{acot}{\left(x \right)} - \pi}{x^{2}}$$
Tercera derivada [src]
  /                                                /         2 \       \
  |                                                |      4*x  |       |
  |                                              2*|-1 + ------|*log(x)|
  |                                                |          2|       |
  |      6       -pi + 2*acot(x)        3          \     1 + x /       |
2*|- --------- - --------------- - ----------- + ----------------------|
  |          2           3          2 /     2\                 2       |
  |  /     2\           x          x *\1 + x /         /     2\        |
  \  \1 + x /                                          \1 + x /        /
$$2 \left(\frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6}{\left(x^{2} + 1\right)^{2}} - \frac{3}{x^{2} \left(x^{2} + 1\right)} - \frac{2 \operatorname{acot}{\left(x \right)} - \pi}{x^{3}}\right)$$
Gráfico
Derivada de (π-2arctgx)lnx