Sr Examen

Otras calculadoras

sqrt(acos(1-(1)/x))^(3)
Derivada de la función/ (1)/x/ sqrt(acos(1-(1)/x))^(3)

Derivada de sqrt(acos(1-(1)/x))^(3)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                 3
    _____________ 
   /     /    1\  
  /  acos|1 - -|  
\/       \    x/
(acos⁡(1−1x))3\left(\sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}\right)^{3} 
(sqrt(acos(1 - 1/x)))^3
Gráfica
02468-8-6-4-2-1010-10050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                3/2/    1\          
         -3*acos   |1 - -|          
                   \    x/          
------------------------------------
          ______________            
         /            2             
   2    /      /    1\       /    1\
2*x *  /   1 - |1 - -|  *acos|1 - -|
     \/        \    x/       \    x/
−3acos⁡32(1−1x)2x21−(1−1x)2acos⁡(1−1x)- \frac{3 \operatorname{acos}^{\frac{3}{2}}{\left(1 - \frac{1}{x} \right)}}{2 x^{2} \sqrt{1 - \left(1 - \frac{1}{x}\right)^{2}} \operatorname{acos}{\left(1 - \frac{1}{x} \right)}}
Simplificar
Segunda derivada [src] 
  /     _____________                                                _____________        \
  |    /     /    1\                                                /     /    1\  /    1\|
  |   /  acos|1 - -|                                               /  acos|1 - -| *|1 - -||
  | \/       \    x/                       1                     \/       \    x/  \    x/|
3*|------------------- - ------------------------------------- - -------------------------|
  |     ______________       /            2\     _____________                       3/2  |
  |    /            2        |     /    1\ |    /     /    1\          /           2\     |
  |   /      /    1\     4*x*|-1 + |1 - -| |*  /  acos|1 - -|          |    /    1\ |     |
  |  /   1 - |1 - -|         \     \    x/ / \/       \    x/      2*x*|1 - |1 - -| |     |
  \\/        \    x/                                                   \    \    x/ /     /
-------------------------------------------------------------------------------------------
                                              3                                            
                                             x
3(acos⁡(1−1x)1−(1−1x)2−(1−1x)acos⁡(1−1x)2x(1−(1−1x)2)32−14x((1−1x)2−1)acos⁡(1−1x))x3\frac{3 \left(\frac{\sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}}{\sqrt{1 - \left(1 - \frac{1}{x}\right)^{2}}} - \frac{\left(1 - \frac{1}{x}\right) \sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}}{2 x \left(1 - \left(1 - \frac{1}{x}\right)^{2}\right)^{\frac{3}{2}}} - \frac{1}{4 x \left(\left(1 - \frac{1}{x}\right)^{2} - 1\right) \sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}}\right)}{x^{3}}
Simplificar
Tercera derivada [src] 
  /        _____________         _____________                                                                                            _____________                    2     _____________                                          \
  |       /     /    1\         /     /    1\                                                                                            /     /    1\  /    1\     /    1\     /     /    1\                     /    1\               |
  |  3*  /  acos|1 - -|        /  acos|1 - -|                                                                                       3*  /  acos|1 - -| *|1 - -|   3*|1 - -| *  /  acos|1 - -|                   3*|1 - -|               |
  |    \/       \    x/      \/       \    x/                         1                                       3                       \/       \    x/  \    x/     \    x/  \/       \    x/                     \    x/               |
3*|- ------------------- - ---------------------- + ------------------------------------- + ------------------------------------- + --------------------------- - ---------------------------- + ---------------------------------------|
  |       ______________                      3/2                      3/2                      /            2\     _____________                       3/2                             5/2                          2                  |
  |      /            2         /           2\           /           2\                         |     /    1\ |    /     /    1\          /           2\                  /           2\              /            2\      _____________|
  |     /      /    1\        2 |    /    1\ |         2 |    /    1\ |        3/2/    1\   2*x*|-1 + |1 - -| |*  /  acos|1 - -|          |    /    1\ |                2 |    /    1\ |            2 |     /    1\ |     /     /    1\ |
  |    /   1 - |1 - -|     2*x *|1 - |1 - -| |      8*x *|1 - |1 - -| |   *acos   |1 - -|       \     \    x/ / \/       \    x/        x*|1 - |1 - -| |             2*x *|1 - |1 - -| |         4*x *|-1 + |1 - -| | *  /  acos|1 - -| |
  \  \/        \    x/          \    \    x/ /           \    \    x/ /           \    x/                                                 \    \    x/ /                  \    \    x/ /              \     \    x/ /  \/       \    x/ /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                     4                                                                                                                   
                                                                                                                    x
3(−3acos⁡(1−1x)1−(1−1x)2+3(1−1x)acos⁡(1−1x)x(1−(1−1x)2)32+32x((1−1x)2−1)acos⁡(1−1x)−3(1−1x)2acos⁡(1−1x)2x2(1−(1−1x)2)52+3(1−1x)4x2((1−1x)2−1)2acos⁡(1−1x)−acos⁡(1−1x)2x2(1−(1−1x)2)32+18x2(1−(1−1x)2)32acos⁡32(1−1x))x4\frac{3 \left(- \frac{3 \sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}}{\sqrt{1 - \left(1 - \frac{1}{x}\right)^{2}}} + \frac{3 \left(1 - \frac{1}{x}\right) \sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}}{x \left(1 - \left(1 - \frac{1}{x}\right)^{2}\right)^{\frac{3}{2}}} + \frac{3}{2 x \left(\left(1 - \frac{1}{x}\right)^{2} - 1\right) \sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}} - \frac{3 \left(1 - \frac{1}{x}\right)^{2} \sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}}{2 x^{2} \left(1 - \left(1 - \frac{1}{x}\right)^{2}\right)^{\frac{5}{2}}} + \frac{3 \left(1 - \frac{1}{x}\right)}{4 x^{2} \left(\left(1 - \frac{1}{x}\right)^{2} - 1\right)^{2} \sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}} - \frac{\sqrt{\operatorname{acos}{\left(1 - \frac{1}{x} \right)}}}{2 x^{2} \left(1 - \left(1 - \frac{1}{x}\right)^{2}\right)^{\frac{3}{2}}} + \frac{1}{8 x^{2} \left(1 - \left(1 - \frac{1}{x}\right)^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{\frac{3}{2}}{\left(1 - \frac{1}{x} \right)}}\right)}{x^{4}}
Simplificar
Gráfico
Derivada de sqrt(acos(1-(1)/x))^(3)
    © Sr Examen – Калькулятор