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xtgx/arctgx
Derivada de la función/ arctg/ xtgx/arctgx

Derivada de xtgx/arctgx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
x*tan(x)
--------
acot(x)
xtan⁡(x)acot⁡(x)\frac{x \tan{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} 
(x*tan(x))/acot(x)
Gráfica
02468-8-6-4-2-1010-2000020000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  /       2   \                             
x*\1 + tan (x)/ + tan(x)        x*tan(x)    
------------------------ + -----------------
        acot(x)            /     2\     2   
                           \1 + x /*acot (x)
xtan⁡(x)(x2+1)acot⁡2(x)+x(tan⁡2(x)+1)+tan⁡(x)acot⁡(x)\frac{x \tan{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}}{\operatorname{acot}{\left(x \right)}}
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Segunda derivada [src] 
  /                                                                    /       1   \       \
  |                                         /       2   \            x*|x - -------|*tan(x)|
  |       2        /       2   \          x*\1 + tan (x)/ + tan(x)     \    acot(x)/       |
2*|1 + tan (x) + x*\1 + tan (x)/*tan(x) + ------------------------ - ----------------------|
  |                                           /     2\                         2           |
  |                                           \1 + x /*acot(x)         /     2\            |
  \                                                                    \1 + x / *acot(x)   /
--------------------------------------------------------------------------------------------
                                          acot(x)
2(−x(x−1acot⁡(x))tan⁡(x)(x2+1)2acot⁡(x)+x(tan⁡2(x)+1)tan⁡(x)+tan⁡2(x)+1+x(tan⁡2(x)+1)+tan⁡(x)(x2+1)acot⁡(x))acot⁡(x)\frac{2 \left(- \frac{x \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \tan^{2}{\left(x \right)} + 1 + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)}{\operatorname{acot}{\left(x \right)}}
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Tercera derivada [src] 
  /                                                                                                                                         /                             2                    \       \
  |                                                                                                                                         |             3            4*x           6*x       |       |
  |                                                                                            /       1   \ /  /       2   \         \   x*|-1 + ----------------- + ------ - ----------------|*tan(x)|
  |                                                 /       2        /       2   \       \   3*|x - -------|*\x*\1 + tan (x)/ + tan(x)/     |     /     2\     2           2   /     2\        |       |
  |/       2   \ /             /         2   \\   3*\1 + tan (x) + x*\1 + tan (x)/*tan(x)/     \    acot(x)/                                \     \1 + x /*acot (x)   1 + x    \1 + x /*acot(x)/       |
2*|\1 + tan (x)/*\3*tan(x) + x*\1 + 3*tan (x)// + ---------------------------------------- - ------------------------------------------ + -------------------------------------------------------------|
  |                                                           /     2\                                           2                                                      2                              |
  |                                                           \1 + x /*acot(x)                           /     2\                                               /     2\                               |
  \                                                                                                      \1 + x / *acot(x)                                      \1 + x / *acot(x)                      /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                acot(x)
2(x(4x2x2+1−6x(x2+1)acot⁡(x)−1+3(x2+1)acot⁡2(x))tan⁡(x)(x2+1)2acot⁡(x)−3(x−1acot⁡(x))(x(tan⁡2(x)+1)+tan⁡(x))(x2+1)2acot⁡(x)+(x(3tan⁡2(x)+1)+3tan⁡(x))(tan⁡2(x)+1)+3(x(tan⁡2(x)+1)tan⁡(x)+tan⁡2(x)+1)(x2+1)acot⁡(x))acot⁡(x)\frac{2 \left(\frac{x \left(\frac{4 x^{2}}{x^{2} + 1} - \frac{6 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - 1 + \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right) \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} - \frac{3 \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \left(x \left(3 \tan^{2}{\left(x \right)} + 1\right) + 3 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{3 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)}{\operatorname{acot}{\left(x \right)}}
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Gráfico
Derivada de xtgx/arctgx
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