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y=arccos((x^2-1)/(x^3+1))
Derivada de la función/ x^2-1/ x^3+1/ (x^2-1)/(x^3+1)/ arccos/ y=arccos((x^2-1)/(x^3+1))

Derivada de y=arccos((x^2-1)/(x^3+1))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    / 2    \
    |x  - 1|
acos|------|
    | 3    |
    \x  + 1/
acos⁡(x2−1x3+1)\operatorname{acos}{\left(\frac{x^{2} - 1}{x^{3} + 1} \right)} 
acos((x^2 - 1)/(x^3 + 1))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 /            2 / 2    \\ 
 | 2*x     3*x *\x  - 1/| 
-|------ - -------------| 
 | 3                 2  | 
 |x  + 1     / 3    \   | 
 \           \x  + 1/   / 
--------------------------
         _______________  
        /             2   
       /      / 2    \    
      /       \x  - 1/    
     /    1 - ---------   
    /                 2   
   /          / 3    \    
 \/           \x  + 1/
−−3x2(x2−1)(x3+1)2+2xx3+1−(x2−1)2(x3+1)2+1- \frac{- \frac{3 x^{2} \left(x^{2} - 1\right)}{\left(x^{3} + 1\right)^{2}} + \frac{2 x}{x^{3} + 1}}{\sqrt{- \frac{\left(x^{2} - 1\right)^{2}}{\left(x^{3} + 1\right)^{2}} + 1}}
Simplificar
Segunda derivada [src] 
 /                                                                      2          \ 
 |                                                  /         /      2\\           | 
 |                                                2 |     3*x*\-1 + x /|  /      2\| 
 |                                               x *|-2 + -------------| *\-1 + x /| 
 |        3        /      2\       4 /      2\      |              3   |           | 
 |    12*x     6*x*\-1 + x /   18*x *\-1 + x /      \         1 + x    /           | 
-|2 - ------ - ------------- + --------------- + ----------------------------------| 
 |         3            3                 2                    /             2\    | 
 |    1 + x        1 + x          /     3\                   2 |    /      2\ |    | 
 |                                \1 + x /           /     3\  |    \-1 + x / |    | 
 |                                                   \1 + x / *|1 - ----------|    | 
 |                                                             |            2 |    | 
 |                                                             |    /     3\  |    | 
 \                                                             \    \1 + x /  /    / 
-------------------------------------------------------------------------------------
                                           ________________                          
                                          /              2                           
                                         /      /      2\                            
                          /     3\      /       \-1 + x /                            
                          \1 + x /*    /    1 - ----------                           
                                      /                 2                            
                                     /          /     3\                             
                                   \/           \1 + x /
−18x4(x2−1)(x3+1)2−12x3x3+1+x2(x2−1)(3x(x2−1)x3+1−2)2(x3+1)2(−(x2−1)2(x3+1)2+1)−6x(x2−1)x3+1+2(x3+1)−(x2−1)2(x3+1)2+1- \frac{\frac{18 x^{4} \left(x^{2} - 1\right)}{\left(x^{3} + 1\right)^{2}} - \frac{12 x^{3}}{x^{3} + 1} + \frac{x^{2} \left(x^{2} - 1\right) \left(\frac{3 x \left(x^{2} - 1\right)}{x^{3} + 1} - 2\right)^{2}}{\left(x^{3} + 1\right)^{2} \left(- \frac{\left(x^{2} - 1\right)^{2}}{\left(x^{3} + 1\right)^{2}} + 1\right)} - \frac{6 x \left(x^{2} - 1\right)}{x^{3} + 1} + 2}{\left(x^{3} + 1\right) \sqrt{- \frac{\left(x^{2} - 1\right)^{2}}{\left(x^{3} + 1\right)^{2}} + 1}}
Simplificar
Tercera derivada [src] 
                                                                                   /                                           2                  2\                                                                                                                           
                                                              /         /      2\\ |                3 /      2\       /      2\        4 /      2\ |                                       3                 /         /      2\\ /        3        /      2\      4 /      2\\
                                                              |     3*x*\-1 + x /| |        2   24*x *\-1 + x /   6*x*\-1 + x /    27*x *\-1 + x / |                 2 /         /      2\\        /      2\ |     3*x*\-1 + x /| |     6*x     3*x*\-1 + x /   9*x *\-1 + x /|
                                                            x*|-2 + -------------|*|-2 + 6*x  - --------------- - -------------- + ----------------|      3 /      2\  |     3*x*\-1 + x /|    4*x*\-1 + x /*|-2 + -------------|*|1 - ------ - ------------- + --------------|
                                                              |              3   | |                      3                3                  2    |   3*x *\-1 + x / *|-2 + -------------|                  |              3   | |         3            3                2   |
                  5        3 /      2\        6 /      2\     \         1 + x    / |                 1 + x            1 + x           /     3\     |                   |              3   |                  \         1 + x    / |    1 + x        1 + x         /     3\    |
         2   108*x    108*x *\-1 + x /   162*x *\-1 + x /                          \                                                  \1 + x /     /                   \         1 + x    /                                       \                               \1 + x /    /
-6 + 60*x  - ------ - ---------------- + ---------------- + ---------------------------------------------------------------------------------------- + ------------------------------------- + --------------------------------------------------------------------------------
                  3             3                   2                                               /             2\                                                                  2                                            /             2\                            
             1 + x         1 + x            /     3\                                                |    /      2\ |                                                  /             2\                                             |    /      2\ |                            
                                            \1 + x /                                       /     3\ |    \-1 + x / |                                                3 |    /      2\ |                                    /     3\ |    \-1 + x / |                            
                                                                                           \1 + x /*|1 - ----------|                                        /     3\  |    \-1 + x / |                                    \1 + x /*|1 - ----------|                            
                                                                                                    |            2 |                                        \1 + x / *|1 - ----------|                                             |            2 |                            
                                                                                                    |    /     3\  |                                                  |            2 |                                             |    /     3\  |                            
                                                                                                    \    \1 + x /  /                                                  |    /     3\  |                                             \    \1 + x /  /                            
                                                                                                                                                                      \    \1 + x /  /                                                                                         
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                         ________________                                                                                                                      
                                                                                                                                        /              2                                                                                                                       
                                                                                                                               2       /      /      2\                                                                                                                        
                                                                                                                       /     3\       /       \-1 + x /                                                                                                                        
                                                                                                                       \1 + x / *    /    1 - ----------                                                                                                                       
                                                                                                                                    /                 2                                                                                                                        
                                                                                                                                   /          /     3\                                                                                                                         
                                                                                                                                 \/           \1 + x /
162x6(x2−1)(x3+1)2−108x5x3+1+3x3(x2−1)2(3x(x2−1)x3+1−2)3(x3+1)3(−(x2−1)2(x3+1)2+1)2−108x3(x2−1)x3+1+60x2+4x(x2−1)(3x(x2−1)x3+1−2)(9x4(x2−1)(x3+1)2−6x3x3+1−3x(x2−1)x3+1+1)(x3+1)(−(x2−1)2(x3+1)2+1)+x(3x(x2−1)x3+1−2)(27x4(x2−1)2(x3+1)2−24x3(x2−1)x3+1+6x2−6x(x2−1)2x3+1−2)(x3+1)(−(x2−1)2(x3+1)2+1)−6(x3+1)2−(x2−1)2(x3+1)2+1\frac{\frac{162 x^{6} \left(x^{2} - 1\right)}{\left(x^{3} + 1\right)^{2}} - \frac{108 x^{5}}{x^{3} + 1} + \frac{3 x^{3} \left(x^{2} - 1\right)^{2} \left(\frac{3 x \left(x^{2} - 1\right)}{x^{3} + 1} - 2\right)^{3}}{\left(x^{3} + 1\right)^{3} \left(- \frac{\left(x^{2} - 1\right)^{2}}{\left(x^{3} + 1\right)^{2}} + 1\right)^{2}} - \frac{108 x^{3} \left(x^{2} - 1\right)}{x^{3} + 1} + 60 x^{2} + \frac{4 x \left(x^{2} - 1\right) \left(\frac{3 x \left(x^{2} - 1\right)}{x^{3} + 1} - 2\right) \left(\frac{9 x^{4} \left(x^{2} - 1\right)}{\left(x^{3} + 1\right)^{2}} - \frac{6 x^{3}}{x^{3} + 1} - \frac{3 x \left(x^{2} - 1\right)}{x^{3} + 1} + 1\right)}{\left(x^{3} + 1\right) \left(- \frac{\left(x^{2} - 1\right)^{2}}{\left(x^{3} + 1\right)^{2}} + 1\right)} + \frac{x \left(\frac{3 x \left(x^{2} - 1\right)}{x^{3} + 1} - 2\right) \left(\frac{27 x^{4} \left(x^{2} - 1\right)^{2}}{\left(x^{3} + 1\right)^{2}} - \frac{24 x^{3} \left(x^{2} - 1\right)}{x^{3} + 1} + 6 x^{2} - \frac{6 x \left(x^{2} - 1\right)^{2}}{x^{3} + 1} - 2\right)}{\left(x^{3} + 1\right) \left(- \frac{\left(x^{2} - 1\right)^{2}}{\left(x^{3} + 1\right)^{2}} + 1\right)} - 6}{\left(x^{3} + 1\right)^{2} \sqrt{- \frac{\left(x^{2} - 1\right)^{2}}{\left(x^{3} + 1\right)^{2}} + 1}}
Simplificar
Gráfico
Derivada de y=arccos((x^2-1)/(x^3+1))
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