Sr Examen

Otras calculadoras

y=arccos(x-x^-1/x+x^-1)
Derivada de la función/ arccos/ x-x^-1/ x+x^-1/ y=arccos(x-x^-1/x+x^-1)

Derivada de y=arccos(x-x^-1/x+x^-1)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /     1    1\
acos|x - --- + -|
    \    x*x   x/
acos⁡((x−1xx)+1x)\operatorname{acos}{\left(\left(x - \frac{1}{x x}\right) + \frac{1}{x} \right)} 
acos(x - 1/(x*x) + 1/x)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      /    1    2 \      
     -|1 - -- + --|      
      |     2    3|      
      \    x    x /      
-------------------------
     ____________________
    /                  2 
   /      /     1    1\  
  /   1 - |x - --- + -|  
\/        \    x*x   x/
−1−1x2+2x31−((x−1xx)+1x)2- \frac{1 - \frac{1}{x^{2}} + \frac{2}{x^{3}}}{\sqrt{1 - \left(\left(x - \frac{1}{x x}\right) + \frac{1}{x}\right)^{2}}}
Simplificar
Segunda derivada [src] 
 /                         2             \ 
 |            /    1    2 \  /    1   1 \| 
 |  /    3\   |1 - -- + --| *|x + - - --|| 
 |2*|1 - -|   |     2    3|  |    x    2|| 
 |  \    x/   \    x    x /  \        x /| 
-|--------- + ---------------------------| 
 |     3                           2     | 
 |    x                /    1   1 \      | 
 |                 1 - |x + - - --|      | 
 |                     |    x    2|      | 
 \                     \        x /      / 
-------------------------------------------
               ___________________         
              /                 2          
             /      /    1   1 \           
            /   1 - |x + - - --|           
           /        |    x    2|           
         \/         \        x /
−(1−1x2+2x3)2(x+1x−1x2)1−(x+1x−1x2)2+2(1−3x)x31−(x+1x−1x2)2- \frac{\frac{\left(1 - \frac{1}{x^{2}} + \frac{2}{x^{3}}\right)^{2} \left(x + \frac{1}{x} - \frac{1}{x^{2}}\right)}{1 - \left(x + \frac{1}{x} - \frac{1}{x^{2}}\right)^{2}} + \frac{2 \left(1 - \frac{3}{x}\right)}{x^{3}}}{\sqrt{1 - \left(x + \frac{1}{x} - \frac{1}{x^{2}}\right)^{2}}}
Simplificar
Tercera derivada [src] 
                 3                               3             2                                       
    /    1    2 \                   /    1    2 \  /    1   1 \      /    3\ /    1    2 \ /    1   1 \
    |1 - -- + --|       /    4\   3*|1 - -- + --| *|x + - - --|    6*|1 - -|*|1 - -- + --|*|x + - - --|
    |     2    3|     6*|1 - -|     |     2    3|  |    x    2|      \    x/ |     2    3| |    x    2|
    \    x    x /       \    x/     \    x    x /  \        x /              \    x    x / \        x /
- ----------------- + --------- - ------------------------------ - ------------------------------------
                  2        4                              2                  /                2\       
      /    1   1 \        x            /                2\                 3 |    /    1   1 \ |       
  1 - |x + - - --|                     |    /    1   1 \ |                x *|1 - |x + - - --| |       
      |    x    2|                     |1 - |x + - - --| |                   |    |    x    2| |       
      \        x /                     |    |    x    2| |                   \    \        x / /       
                                       \    \        x / /                                             
-------------------------------------------------------------------------------------------------------
                                             ___________________                                       
                                            /                 2                                        
                                           /      /    1   1 \                                         
                                          /   1 - |x + - - --|                                         
                                         /        |    x    2|                                         
                                       \/         \        x /
−(1−1x2+2x3)31−(x+1x−1x2)2−3(1−1x2+2x3)3(x+1x−1x2)2(1−(x+1x−1x2)2)2−6(1−3x)(1−1x2+2x3)(x+1x−1x2)x3(1−(x+1x−1x2)2)+6(1−4x)x41−(x+1x−1x2)2\frac{- \frac{\left(1 - \frac{1}{x^{2}} + \frac{2}{x^{3}}\right)^{3}}{1 - \left(x + \frac{1}{x} - \frac{1}{x^{2}}\right)^{2}} - \frac{3 \left(1 - \frac{1}{x^{2}} + \frac{2}{x^{3}}\right)^{3} \left(x + \frac{1}{x} - \frac{1}{x^{2}}\right)^{2}}{\left(1 - \left(x + \frac{1}{x} - \frac{1}{x^{2}}\right)^{2}\right)^{2}} - \frac{6 \left(1 - \frac{3}{x}\right) \left(1 - \frac{1}{x^{2}} + \frac{2}{x^{3}}\right) \left(x + \frac{1}{x} - \frac{1}{x^{2}}\right)}{x^{3} \left(1 - \left(x + \frac{1}{x} - \frac{1}{x^{2}}\right)^{2}\right)} + \frac{6 \left(1 - \frac{4}{x}\right)}{x^{4}}}{\sqrt{1 - \left(x + \frac{1}{x} - \frac{1}{x^{2}}\right)^{2}}}
Simplificar
Gráfico
Derivada de y=arccos(x-x^-1/x+x^-1)
    © Sr Examen – Калькулятор