Sr Examen

Otras calculadoras

atan((2*x+1)/(2*x-1))
Derivada de la función/ 2*x-1/ 2*x+1/ atan((2*x+1)/(2*x-1))

Derivada de atan((2*x+1)/(2*x-1))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /2*x + 1\
atan|-------|
    \2*x - 1/
atan⁡(2x+12x−1)\operatorname{atan}{\left(\frac{2 x + 1}{2 x - 1} \right)} 
atan((2*x + 1)/(2*x - 1))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   2      2*(2*x + 1)
------- - -----------
2*x - 1             2
           (2*x - 1) 
---------------------
                 2   
        (2*x + 1)    
    1 + ----------   
                 2   
        (2*x - 1)
22x−1−2(2x+1)(2x−1)21+(2x+1)2(2x−1)2\frac{\frac{2}{2 x - 1} - \frac{2 \left(2 x + 1\right)}{\left(2 x - 1\right)^{2}}}{1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}}
Simplificar
Segunda derivada [src] 
                  /                /    1 + 2*x \  \
                  |      (1 + 2*x)*|1 - --------|  |
   /    1 + 2*x \ |                \    -1 + 2*x/  |
-8*|1 - --------|*|1 + ----------------------------|
   \    -1 + 2*x/ |    /              2\           |
                  |    |     (1 + 2*x) |           |
                  |    |1 + -----------|*(-1 + 2*x)|
                  |    |              2|           |
                  \    \    (-1 + 2*x) /           /
----------------------------------------------------
           /              2\                        
           |     (1 + 2*x) |           2            
           |1 + -----------|*(-1 + 2*x)             
           |              2|                        
           \    (-1 + 2*x) /
−8(1−2x+12x−1)(1+(1−2x+12x−1)(2x+1)(1+(2x+1)2(2x−1)2)(2x−1))(1+(2x+1)2(2x−1)2)(2x−1)2- \frac{8 \left(1 - \frac{2 x + 1}{2 x - 1}\right) \left(1 + \frac{\left(1 - \frac{2 x + 1}{2 x - 1}\right) \left(2 x + 1\right)}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right) \left(2 x - 1\right)}\right)}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right) \left(2 x - 1\right)^{2}}
Simplificar
Tercera derivada [src] 
                  /                                 2                                                                \
                  |        4*(1 + 2*x)   3*(1 + 2*x)                                2                                |
                  |    1 - ----------- + ------------               2 /    1 + 2*x \                  /    1 + 2*x \ |
                  |          -1 + 2*x              2     4*(1 + 2*x) *|1 - --------|      4*(1 + 2*x)*|1 - --------| |
   /    1 + 2*x \ |                      (-1 + 2*x)                   \    -1 + 2*x/                  \    -1 + 2*x/ |
16*|1 - --------|*|3 - ------------------------------ + ------------------------------ + ----------------------------|
   \    -1 + 2*x/ |                         2                            2               /              2\           |
                  |                (1 + 2*x)            /              2\                |     (1 + 2*x) |           |
                  |           1 + -----------           |     (1 + 2*x) |            2   |1 + -----------|*(-1 + 2*x)|
                  |                         2           |1 + -----------| *(-1 + 2*x)    |              2|           |
                  |               (-1 + 2*x)            |              2|                \    (-1 + 2*x) /           |
                  \                                     \    (-1 + 2*x) /                                            /
----------------------------------------------------------------------------------------------------------------------
                                            /              2\                                                         
                                            |     (1 + 2*x) |           3                                             
                                            |1 + -----------|*(-1 + 2*x)                                              
                                            |              2|                                                         
                                            \    (-1 + 2*x) /
16(1−2x+12x−1)(3+4(1−2x+12x−1)(2x+1)(1+(2x+1)2(2x−1)2)(2x−1)−1−4(2x+1)2x−1+3(2x+1)2(2x−1)21+(2x+1)2(2x−1)2+4(1−2x+12x−1)2(2x+1)2(1+(2x+1)2(2x−1)2)2(2x−1)2)(1+(2x+1)2(2x−1)2)(2x−1)3\frac{16 \left(1 - \frac{2 x + 1}{2 x - 1}\right) \left(3 + \frac{4 \left(1 - \frac{2 x + 1}{2 x - 1}\right) \left(2 x + 1\right)}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right) \left(2 x - 1\right)} - \frac{1 - \frac{4 \left(2 x + 1\right)}{2 x - 1} + \frac{3 \left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}}{1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}} + \frac{4 \left(1 - \frac{2 x + 1}{2 x - 1}\right)^{2} \left(2 x + 1\right)^{2}}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right)^{2} \left(2 x - 1\right)^{2}}\right)}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right) \left(2 x - 1\right)^{3}}
Simplificar
Gráfico
Derivada de atan((2*x+1)/(2*x-1))
    © Sr Examen – Калькулятор