Sr Examen

Derivada de π*arctgx/arcctgx

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

Gráfico:

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Solución

Ha introducido [src]
pi*acot(x)
----------
 acot(x)  
$$\frac{\pi \operatorname{acot}{\left(x \right)}}{\operatorname{acot}{\left(x \right)}}$$
(pi*acot(x))/acot(x)
Gráfica
Primera derivada [src]
0
$$0$$
Segunda derivada [src]
0
$$0$$
Tercera derivada [src]
     /                                         /       1   \ \
     |                                       3*|x - -------| |
     |        3                 3*x            \    acot(x)/ |
2*pi*|----------------- - ---------------- + ----------------|
     |/     2\     2      /     2\           /     2\        |
     \\1 + x /*acot (x)   \1 + x /*acot(x)   \1 + x /*acot(x)/
--------------------------------------------------------------
                              2                               
                      /     2\                                
                      \1 + x / *acot(x)                       
$$\frac{2 \pi \left(- \frac{3 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{3 \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right)}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}}$$
Gráfico
Derivada de π*arctgx/arcctgx