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y=lnarctg((1)/(1+x))
Derivada de la función/ arctg/ (1+x)/ y=lnarctg((1)/(1+x))

Derivada de y=lnarctg((1)/(1+x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
           /  1  \
log(x)*atan|-----|
           \1 + x/
log⁡(x)atan⁡(1x+1)\log{\left(x \right)} \operatorname{atan}{\left(\frac{1}{x + 1} \right)} 
log(x)*atan(1/(1 + x))
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
    /  1  \                          
atan|-----|                          
    \1 + x/            log(x)        
----------- - -----------------------
     x               2 /       1    \
              (1 + x) *|1 + --------|
                       |           2|
                       \    (1 + x) /
−log⁡(x)(1+1(x+1)2)(x+1)2+atan⁡(1x+1)x- \frac{\log{\left(x \right)}}{\left(1 + \frac{1}{\left(x + 1\right)^{2}}\right) \left(x + 1\right)^{2}} + \frac{\operatorname{atan}{\left(\frac{1}{x + 1} \right)}}{x}
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Segunda derivada [src] 
                                              /               1           \       
                                            2*|1 - -----------------------|*log(x)
                                              |           2 /       1    \|       
      /  1  \                                 |    (1 + x) *|1 + --------||       
  atan|-----|                                 |             |           2||       
      \1 + x/               2                 \             \    (1 + x) //       
- ----------- - ------------------------- + --------------------------------------
        2                2 /       1    \                 3 /       1    \        
       x        x*(1 + x) *|1 + --------|          (1 + x) *|1 + --------|        
                           |           2|                   |           2|        
                           \    (1 + x) /                   \    (1 + x) /
2(1−1(1+1(x+1)2)(x+1)2)log⁡(x)(1+1(x+1)2)(x+1)3−2x(1+1(x+1)2)(x+1)2−atan⁡(1x+1)x2\frac{2 \left(1 - \frac{1}{\left(1 + \frac{1}{\left(x + 1\right)^{2}}\right) \left(x + 1\right)^{2}}\right) \log{\left(x \right)}}{\left(1 + \frac{1}{\left(x + 1\right)^{2}}\right) \left(x + 1\right)^{3}} - \frac{2}{x \left(1 + \frac{1}{\left(x + 1\right)^{2}}\right) \left(x + 1\right)^{2}} - \frac{\operatorname{atan}{\left(\frac{1}{x + 1} \right)}}{x^{2}}
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Tercera derivada [src] 
                                               /               7                         4            \                                         
                                             2*|3 - ----------------------- + ------------------------|*log(x)     /               1           \
                                               |           2 /       1    \                          2|          6*|1 - -----------------------|
                                               |    (1 + x) *|1 + --------|          4 /       1    \ |            |           2 /       1    \|
      /  1  \                                  |             |           2|   (1 + x) *|1 + --------| |            |    (1 + x) *|1 + --------||
2*atan|-----|                                  |             \    (1 + x) /            |           2| |            |             |           2||
      \1 + x/               3                  \                                       \    (1 + x) / /            \             \    (1 + x) //
------------- + -------------------------- - ----------------------------------------------------------------- + -------------------------------
       3         2        2 /       1    \                               4 /       1    \                                    3 /       1    \   
      x         x *(1 + x) *|1 + --------|                        (1 + x) *|1 + --------|                           x*(1 + x) *|1 + --------|   
                            |           2|                                 |           2|                                      |           2|   
                            \    (1 + x) /                                 \    (1 + x) /                                      \    (1 + x) /
−2(3−7(1+1(x+1)2)(x+1)2+4(1+1(x+1)2)2(x+1)4)log⁡(x)(1+1(x+1)2)(x+1)4+6(1−1(1+1(x+1)2)(x+1)2)x(1+1(x+1)2)(x+1)3+3x2(1+1(x+1)2)(x+1)2+2atan⁡(1x+1)x3- \frac{2 \left(3 - \frac{7}{\left(1 + \frac{1}{\left(x + 1\right)^{2}}\right) \left(x + 1\right)^{2}} + \frac{4}{\left(1 + \frac{1}{\left(x + 1\right)^{2}}\right)^{2} \left(x + 1\right)^{4}}\right) \log{\left(x \right)}}{\left(1 + \frac{1}{\left(x + 1\right)^{2}}\right) \left(x + 1\right)^{4}} + \frac{6 \left(1 - \frac{1}{\left(1 + \frac{1}{\left(x + 1\right)^{2}}\right) \left(x + 1\right)^{2}}\right)}{x \left(1 + \frac{1}{\left(x + 1\right)^{2}}\right) \left(x + 1\right)^{3}} + \frac{3}{x^{2} \left(1 + \frac{1}{\left(x + 1\right)^{2}}\right) \left(x + 1\right)^{2}} + \frac{2 \operatorname{atan}{\left(\frac{1}{x + 1} \right)}}{x^{3}}
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Gráfico
Derivada de y=lnarctg((1)/(1+x))
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