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π-4arctg(1/(x+1))
Derivada de la función/ (x+1)/ arctg/ π-4arctg(1/(x+1))

Derivada de π-4arctg(1/(x+1))

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

Gráfico:

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Definida a trozos:

Solución

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