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atan(1/(x-1))
Derivada de la función/ (x-1)/ atan(1/(x-1))

Derivada de atan(1/(x-1))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /  1  \
atan|-----|
    \x - 1/
atan⁡(1x−1)\operatorname{atan}{\left(\frac{1}{x - 1} \right)} 
atan(1/(x - 1))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
          -1           
-----------------------
/       1    \        2
|1 + --------|*(x - 1) 
|           2|         
\    (x - 1) /
−1(1+1(x−1)2)(x−1)2- \frac{1}{\left(1 + \frac{1}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)^{2}}
Simplificar
Segunda derivada [src] 
  /                1            \
2*|1 - -------------------------|
  |    /        1    \         2|
  |    |1 + ---------|*(-1 + x) |
  |    |            2|          |
  \    \    (-1 + x) /          /
---------------------------------
    /        1    \         3    
    |1 + ---------|*(-1 + x)     
    |            2|              
    \    (-1 + x) /
2(1−1(1+1(x−1)2)(x−1)2)(1+1(x−1)2)(x−1)3\frac{2 \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] 
  /                 4                            7            \
2*|-3 - -------------------------- + -------------------------|
  |                    2             /        1    \         2|
  |     /        1    \          4   |1 + ---------|*(-1 + x) |
  |     |1 + ---------| *(-1 + x)    |            2|          |
  |     |            2|              \    (-1 + x) /          |
  \     \    (-1 + x) /                                       /
---------------------------------------------------------------
                   /        1    \         4                   
                   |1 + ---------|*(-1 + x)                    
                   |            2|                             
                   \    (-1 + x) /
2(−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{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)}{\left(1 + \frac{1}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)^{4}}
Simplificar
Gráfico
Derivada de atan(1/(x-1))
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