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(-x)/(sqrt(1-x^2)+acos(x))
Derivada de la función/ cos(x)/ 1-x^2/ sqrt(1-x^2)+acos(x)/ (-x)/(sqrt(1-x^2)+acos(x))

Derivada de (-x)/(sqrt(1-x^2)+acos(x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
         -x          
---------------------
   ________          
  /      2           
\/  1 - x   + acos(x)
(−1)x1−x2+acos⁡(x)\frac{\left(-1\right) x}{\sqrt{1 - x^{2}} + \operatorname{acos}{\left(x \right)}} 
(-x)/(sqrt(1 - x^2) + acos(x))
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                            /     1             x     \
                          x*|----------- + -----------|
                            |   ________      ________|
                            |  /      2      /      2 |
            1               \\/  1 - x     \/  1 - x  /
- --------------------- - -----------------------------
     ________                                       2  
    /      2                 /   ________          \   
  \/  1 - x   + acos(x)      |  /      2           |   
                             \\/  1 - x   + acos(x)/
−x(x1−x2+11−x2)(1−x2+acos⁡(x))2−11−x2+acos⁡(x)- \frac{x \left(\frac{x}{\sqrt{1 - x^{2}}} + \frac{1}{\sqrt{1 - x^{2}}}\right)}{\left(\sqrt{1 - x^{2}} + \operatorname{acos}{\left(x \right)}\right)^{2}} - \frac{1}{\sqrt{1 - x^{2}} + \operatorname{acos}{\left(x \right)}}
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Segunda derivada [src] 
  /                   2                                      \              
  |        x         x                                       |              
  |-1 + ------- + -------                                    |              
  |           2         2                        2           |              
  |     -1 + x    -1 + x                2*(1 + x)            |    2*(1 + x) 
x*|---------------------- + ---------------------------------| - -----------
  |        ________                   /   ________          \|      ________
  |       /      2          /      2\ |  /      2           ||     /      2 
  \     \/  1 - x           \-1 + x /*\\/  1 - x   + acos(x)//   \/  1 - x  
----------------------------------------------------------------------------
                                                 2                          
                          /   ________          \                           
                          |  /      2           |                           
                          \\/  1 - x   + acos(x)/
x(2(x+1)2(x2−1)(1−x2+acos⁡(x))+x2x2−1+xx2−1−11−x2)−2(x+1)1−x2(1−x2+acos⁡(x))2\frac{x \left(\frac{2 \left(x + 1\right)^{2}}{\left(x^{2} - 1\right) \left(\sqrt{1 - x^{2}} + \operatorname{acos}{\left(x \right)}\right)} + \frac{\frac{x^{2}}{x^{2} - 1} + \frac{x}{x^{2} - 1} - 1}{\sqrt{1 - x^{2}}}\right) - \frac{2 \left(x + 1\right)}{\sqrt{1 - x^{2}}}}{\left(\sqrt{1 - x^{2}} + \operatorname{acos}{\left(x \right)}\right)^{2}}
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Tercera derivada [src] 
    /                  2         3                                                     /                   2  \\     /                   2  \                                    
    |               3*x       3*x                                                      |        x         x   ||     |        x         x   |                                    
    |  -1 - 3*x + ------- + -------                                          6*(1 + x)*|-1 + ------- + -------||   3*|-1 + ------- + -------|                                    
    |                   2         2                         3                          |           2         2||     |           2         2|                        2           
    |             -1 + x    -1 + x                 6*(1 + x)                           \     -1 + x    -1 + x /|     \     -1 + x    -1 + x /               6*(1 + x)            
- x*|- ---------------------------- + ------------------------------------ + ----------------------------------| + -------------------------- + ---------------------------------
    |                  3/2                                               2             /   ________          \ |             ________                     /   ________          \
    |          /     2\                       3/2 /   ________          \    /      2\ |  /      2           | |            /      2            /      2\ |  /      2           |
    |          \1 - x /               /     2\    |  /      2           |    \-1 + x /*\\/  1 - x   + acos(x)/ |          \/  1 - x             \-1 + x /*\\/  1 - x   + acos(x)/
    \                                 \1 - x /   *\\/  1 - x   + acos(x)/                                      /                                                                 
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                    2                                                                            
                                                                             /   ________          \                                                                             
                                                                             |  /      2           |                                                                             
                                                                             \\/  1 - x   + acos(x)/
−x(6(x+1)(x2x2−1+xx2−1−1)(x2−1)(1−x2+acos⁡(x))+6(x+1)3(1−x2)32(1−x2+acos⁡(x))2−3x3x2−1+3x2x2−1−3x−1(1−x2)32)+6(x+1)2(x2−1)(1−x2+acos⁡(x))+3(x2x2−1+xx2−1−1)1−x2(1−x2+acos⁡(x))2\frac{- x \left(\frac{6 \left(x + 1\right) \left(\frac{x^{2}}{x^{2} - 1} + \frac{x}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right) \left(\sqrt{1 - x^{2}} + \operatorname{acos}{\left(x \right)}\right)} + \frac{6 \left(x + 1\right)^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\sqrt{1 - x^{2}} + \operatorname{acos}{\left(x \right)}\right)^{2}} - \frac{\frac{3 x^{3}}{x^{2} - 1} + \frac{3 x^{2}}{x^{2} - 1} - 3 x - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) + \frac{6 \left(x + 1\right)^{2}}{\left(x^{2} - 1\right) \left(\sqrt{1 - x^{2}} + \operatorname{acos}{\left(x \right)}\right)} + \frac{3 \left(\frac{x^{2}}{x^{2} - 1} + \frac{x}{x^{2} - 1} - 1\right)}{\sqrt{1 - x^{2}}}}{\left(\sqrt{1 - x^{2}} + \operatorname{acos}{\left(x \right)}\right)^{2}}
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Gráfico
Derivada de (-x)/(sqrt(1-x^2)+acos(x))
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