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y=(xarccosx)/arccotx
Derivada de la función/ arccos/ y=(xarccosx)/arccotx

Derivada de y=(xarccosx)/arccotx

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
x*acos(x)
---------
 acot(x)
xacos⁡(x)acot⁡(x)\frac{x \operatorname{acos}{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} 
(x*acos(x))/acot(x)
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       x                                   
- ----------- + acos(x)                    
     ________                              
    /      2                               
  \/  1 - x                   x*acos(x)    
----------------------- + -----------------
        acot(x)           /     2\     2   
                          \1 + x /*acot (x)
xacos⁡(x)(x2+1)acot⁡2(x)+−x1−x2+acos⁡(x)acot⁡(x)\frac{x \operatorname{acos}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} + \frac{- \frac{x}{\sqrt{1 - x^{2}}} + \operatorname{acos}{\left(x \right)}}{\operatorname{acot}{\left(x \right)}}
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Segunda derivada [src] 
         2       /                x     \                            
        x      2*|-acos(x) + -----------|                            
-2 + -------     |              ________|       /       1   \        
           2     |             /      2 |   2*x*|x - -------|*acos(x)
     -1 + x      \           \/  1 - x  /       \    acot(x)/        
------------ - -------------------------- - -------------------------
   ________         /     2\                            2            
  /      2          \1 + x /*acot(x)            /     2\             
\/  1 - x                                       \1 + x / *acot(x)    
---------------------------------------------------------------------
                               acot(x)
−2x(x−1acot⁡(x))acos⁡(x)(x2+1)2acot⁡(x)−2(x1−x2−acos⁡(x))(x2+1)acot⁡(x)+x2x2−1−21−x2acot⁡(x)\frac{- \frac{2 x \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \operatorname{acos}{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} - \frac{2 \left(\frac{x}{\sqrt{1 - x^{2}}} - \operatorname{acos}{\left(x \right)}\right)}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{\frac{x^{2}}{x^{2} - 1} - 2}{\sqrt{1 - x^{2}}}}{\operatorname{acot}{\left(x \right)}}
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Tercera derivada [src] 
  /          2 \           /         2  \           /       1   \ /                x     \       /                             2                    \        
  |       3*x  |           |        x   |         6*|x - -------|*|-acos(x) + -----------|       |             3            4*x           6*x       |        
x*|-4 + -------|         3*|-2 + -------|           \    acot(x)/ |              ________|   2*x*|-1 + ----------------- + ------ - ----------------|*acos(x)
  |           2|           |           2|                         |             /      2 |       |     /     2\     2           2   /     2\        |        
  \     -1 + x /           \     -1 + x /                         \           \/  1 - x  /       \     \1 + x /*acot (x)   1 + x    \1 + x /*acot(x)/        
---------------- + ---------------------------- + ---------------------------------------- + ----------------------------------------------------------------
          3/2                  ________                              2                                                      2                                
  /     2\         /     2\   /      2                       /     2\                                               /     2\                                 
  \1 - x /         \1 + x /*\/  1 - x  *acot(x)              \1 + x / *acot(x)                                      \1 + x / *acot(x)                        
-------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                           acot(x)
2x(4x2x2+1−6x(x2+1)acot⁡(x)−1+3(x2+1)acot⁡2(x))acos⁡(x)(x2+1)2acot⁡(x)+x(3x2x2−1−4)(1−x2)32+6(x−1acot⁡(x))(x1−x2−acos⁡(x))(x2+1)2acot⁡(x)+3(x2x2−1−2)1−x2(x2+1)acot⁡(x)acot⁡(x)\frac{\frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - \frac{6 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - 1 + \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right) \operatorname{acos}{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \frac{x \left(\frac{3 x^{2}}{x^{2} - 1} - 4\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6 \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \left(\frac{x}{\sqrt{1 - x^{2}}} - \operatorname{acos}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \frac{3 \left(\frac{x^{2}}{x^{2} - 1} - 2\right)}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}}{\operatorname{acot}{\left(x \right)}}
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Gráfico
Derivada de y=(xarccosx)/arccotx
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