Sr Examen

Otras calculadoras

y=arctg^3(lnx^1/2/x+2)

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de x^12 Derivada de x^12
  • Derivada de (x+3)/(x-2) Derivada de (x+3)/(x-2)
  • Derivada de e^3 Derivada de e^3
  • Derivada de x!

  • Expresiones idénticas

  • y=arctg^ tres (lnx^ uno / dos /x+ dos)
  • y es igual a arctg al cubo (lnx en el grado 1 dividir por 2 dividir por x más 2)
  • y es igual a arctg en el grado tres (lnx en el grado uno dividir por dos dividir por x más dos)
  • y=arctg3(lnx1/2/x+2)
  • y=arctg3lnx1/2/x+2
  • y=arctg³(lnx^1/2/x+2)
  • y=arctg en el grado 3(lnx en el grado 1/2/x+2)
  • y=arctg^3lnx^1/2/x+2
  • y=arctg^3(lnx^1 dividir por 2 dividir por x+2)

  • Expresiones semejantes

  • y=arctg^3(lnx^1/2/x-2)

  • Expresiones con funciones

  • arctg
  • arctg^2(1/x)
Derivada de la función/ arctg/ x^1/2/ y=arctg^3(lnx^1/2/x+2)

Derivada de y=arctg^3(lnx^1/2/x+2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     /  ________    \
    3|\/ log(x)     |
atan |---------- + 2|
     \    x         /
atan⁡3(2+log⁡(x)x)\operatorname{atan}^{3}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)} 
atan(sqrt(log(x))/x + 2)^3
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       /  ________    \ /                    ________\
      2|\/ log(x)     | |       1          \/ log(x) |
3*atan |---------- + 2|*|--------------- - ----------|
       \    x         / |   2   ________        2    |
                        \2*x *\/ log(x)        x     /
------------------------------------------------------
                                    2                 
                    /  ________    \                  
                    |\/ log(x)     |                  
                1 + |---------- + 2|                  
                    \    x         /
3(−log⁡(x)x2+12x2log⁡(x))atan⁡2(2+log⁡(x)x)(2+log⁡(x)x)2+1\frac{3 \left(- \frac{\sqrt{\log{\left(x \right)}}}{x^{2}} + \frac{1}{2 x^{2} \sqrt{\log{\left(x \right)}}}\right) \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1}
Simplificar
Segunda derivada [src] 
  /                                                                                                2                                  2 /      ________\     /      ________\\                     
  |                                                                   /      1            ________\      /      1            ________\  |    \/ log(x) |     |    \/ log(x) ||                     
  |                                                                 2*|- ---------- + 2*\/ log(x) |    2*|- ---------- + 2*\/ log(x) | *|2 + ----------|*atan|2 + ----------||                     
  |                                              /      ________\     |    ________               |      |    ________               |  \        x     /     \        x     /|     /      ________\
  |  /    1           ________       6     \     |    \/ log(x) |     \  \/ log(x)                /      \  \/ log(x)                /                                       |     |    \/ log(x) |
3*|- |--------- - 8*\/ log(x)  + ----------|*atan|2 + ----------| + -------------------------------- - ----------------------------------------------------------------------|*atan|2 + ----------|
  |  |   3/2                       ________|     \        x     /        /                    2\                               /                    2\                       |     \        x     /
  |  \log   (x)                  \/ log(x) /                             |    /      ________\ |                               |    /      ________\ |                       |                     
  |                                                                      |    |    \/ log(x) | |                               |    |    \/ log(x) | |                       |                     
  |                                                                    x*|1 + |2 + ----------| |                             x*|1 + |2 + ----------| |                       |                     
  \                                                                      \    \        x     / /                               \    \        x     / /                       /                     
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                         /                    2\                                                                                   
                                                                                         |    /      ________\ |                                                                                   
                                                                                       3 |    |    \/ log(x) | |                                                                                   
                                                                                    4*x *|1 + |2 + ----------| |                                                                                   
                                                                                         \    \        x     / /
3(−(−8log⁡(x)+6log⁡(x)+1log⁡(x)32)atan⁡(2+log⁡(x)x)−2(2+log⁡(x)x)(2log⁡(x)−1log⁡(x))2atan⁡(2+log⁡(x)x)x((2+log⁡(x)x)2+1)+2(2log⁡(x)−1log⁡(x))2x((2+log⁡(x)x)2+1))atan⁡(2+log⁡(x)x)4x3((2+log⁡(x)x)2+1)\frac{3 \left(- \left(- 8 \sqrt{\log{\left(x \right)}} + \frac{6}{\sqrt{\log{\left(x \right)}}} + \frac{1}{\log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)} - \frac{2 \left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right) \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{2} \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{x \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)} + \frac{2 \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{2}}{x \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)}\right) \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{4 x^{3} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)}
Simplificar
Tercera derivada [src] 
  /                                                                                                                                                                                       2                                                                                                                                                                                                                                                                                                                                              \
  |     /      ________\                                                                                       3                                3      /      ________\   /      ________\                               3      /      ________\                                  3 /      ________\     /      ________\                                                                               /      ________\          /      ________\ /      ________\                                                                      |
  |    2|    \/ log(x) | /       ________       3           12          44    \   /      1            ________\    /      1            ________\      2|    \/ log(x) |   |    \/ log(x) |  /      1            ________\      2|    \/ log(x) |     /      1            ________\  |    \/ log(x) |     |    \/ log(x) |     /      1            ________\ /    1           ________       6     \     |    \/ log(x) |         2|    \/ log(x) | |    \/ log(x) | /      1            ________\ /    1           ________       6     \|
  |atan |2 + ----------|*|- 48*\/ log(x)  + --------- + --------- + ----------|   |- ---------- + 2*\/ log(x) |    |- ---------- + 2*\/ log(x) | *atan |2 + ----------|   |2 + ----------| *|- ---------- + 2*\/ log(x) | *atan |2 + ----------|   3*|- ---------- + 2*\/ log(x) | *|2 + ----------|*atan|2 + ----------|   3*|- ---------- + 2*\/ log(x) |*|--------- - 8*\/ log(x)  + ----------|*atan|2 + ----------|   3*atan |2 + ----------|*|2 + ----------|*|- ---------- + 2*\/ log(x) |*|--------- - 8*\/ log(x)  + ----------||
  |     \        x     / |                     5/2         3/2        ________|   |    ________               |    |    ________               |       \        x     /   \        x     /  |    ________               |       \        x     /     |    ________               |  \        x     /     \        x     /     |    ________               | |   3/2                       ________|     \        x     /          \        x     / \        x     / |    ________               | |   3/2                       ________||
  |                      \                  log   (x)   log   (x)   \/ log(x) /   \  \/ log(x)                /    \  \/ log(x)                /                                            \  \/ log(x)                /                            \  \/ log(x)                /                                            \  \/ log(x)                / \log   (x)                  \/ log(x) /                                                                 \  \/ log(x)                / \log   (x)                  \/ log(x) /|
3*|---------------------------------------------------------------------------- - ------------------------------ + ---------------------------------------------------- - ---------------------------------------------------------------------- + ---------------------------------------------------------------------- + -------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------|
  |                                     8                                                                     2                     /                    2\                                                              2                                                                         2                                                            /                    2\                                                                                 /                    2\                                          |
  |                                                                                    /                    2\                      |    /      ________\ |                                       /                    2\                                                   /                    2\                                                             |    /      ________\ |                                                                                 |    /      ________\ |                                          |
  |                                                                                    |    /      ________\ |                    2 |    |    \/ log(x) | |                                       |    /      ________\ |                                                   |    /      ________\ |                                                             |    |    \/ log(x) | |                                                                                 |    |    \/ log(x) | |                                          |
  |                                                                                  2 |    |    \/ log(x) | |                 4*x *|1 + |2 + ----------| |                                     2 |    |    \/ log(x) | |                                                 2 |    |    \/ log(x) | |                                                         4*x*|1 + |2 + ----------| |                                                                             4*x*|1 + |2 + ----------| |                                          |
  |                                                                               4*x *|1 + |2 + ----------| |                      \    \        x     / /                                    x *|1 + |2 + ----------| |                                              2*x *|1 + |2 + ----------| |                                                             \    \        x     / /                                                                                 \    \        x     / /                                          |
  \                                                                                    \    \        x     / /                                                                                    \    \        x     / /                                                   \    \        x     / /                                                                                                                                                                                                                                      /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                           /                    2\                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                           |    /      ________\ |                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                         4 |    |    \/ log(x) | |                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                        x *|1 + |2 + ----------| |                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                           \    \        x     / /
3((−48log⁡(x)+44log⁡(x)+12log⁡(x)32+3log⁡(x)52)atan⁡2(2+log⁡(x)x)8−3(2+log⁡(x)x)(2log⁡(x)−1log⁡(x))(−8log⁡(x)+6log⁡(x)+1log⁡(x)32)atan⁡2(2+log⁡(x)x)4x((2+log⁡(x)x)2+1)+3(2log⁡(x)−1log⁡(x))(−8log⁡(x)+6log⁡(x)+1log⁡(x)32)atan⁡(2+log⁡(x)x)4x((2+log⁡(x)x)2+1)−(2+log⁡(x)x)2(2log⁡(x)−1log⁡(x))3atan⁡2(2+log⁡(x)x)x2((2+log⁡(x)x)2+1)2+3(2+log⁡(x)x)(2log⁡(x)−1log⁡(x))3atan⁡(2+log⁡(x)x)2x2((2+log⁡(x)x)2+1)2+(2log⁡(x)−1log⁡(x))3atan⁡2(2+log⁡(x)x)4x2((2+log⁡(x)x)2+1)−(2log⁡(x)−1log⁡(x))34x2((2+log⁡(x)x)2+1)2)x4((2+log⁡(x)x)2+1)\frac{3 \left(\frac{\left(- 48 \sqrt{\log{\left(x \right)}} + \frac{44}{\sqrt{\log{\left(x \right)}}} + \frac{12}{\log{\left(x \right)}^{\frac{3}{2}}} + \frac{3}{\log{\left(x \right)}^{\frac{5}{2}}}\right) \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{8} - \frac{3 \left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right) \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right) \left(- 8 \sqrt{\log{\left(x \right)}} + \frac{6}{\sqrt{\log{\left(x \right)}}} + \frac{1}{\log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{4 x \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)} + \frac{3 \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right) \left(- 8 \sqrt{\log{\left(x \right)}} + \frac{6}{\sqrt{\log{\left(x \right)}}} + \frac{1}{\log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{4 x \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)} - \frac{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{3} \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{x^{2} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)^{2}} + \frac{3 \left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right) \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{3} \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{2 x^{2} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)^{2}} + \frac{\left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{3} \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{4 x^{2} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)} - \frac{\left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{3}}{4 x^{2} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)^{2}}\right)}{x^{4} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)}
Simplificar
Gráfico
Derivada de y=arctg^3(lnx^1/2/x+2)
    © Sr Examen – Калькулятор