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y=arccos((4x^2-1)/(sqrt(2)*4x^2))
Derivada de la función/ y=arccos((4x^2-1)/(sqrt(2)*4x^2))

Derivada de y=arccos((4x^2-1)/(sqrt(2)*4x^2))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /    2     \
    | 4*x  - 1 |
acos|----------|
    |  ___    2|
    \\/ 2 *4*x /
acos⁡(4x2−1x2⋅42)\operatorname{acos}{\left(\frac{4 x^{2} - 1}{x^{2} \cdot 4 \sqrt{2}} \right)} 
acos((4*x^2 - 1)/(((sqrt(2)*4)*x^2)))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 /      ___     ___ /   2    \\ 
 |    \/ 2    \/ 2 *\4*x  - 1/| 
-|8*x*----- - ----------------| 
 |        2            3      | 
 \     8*x          4*x       / 
--------------------------------
           _________________    
          /               2     
         /      /   2    \      
        /       \4*x  - 1/      
       /    1 - -----------     
      /                4        
    \/             32*x
−8x28x2−2(4x2−1)4x31−(4x2−1)232x4- \frac{8 x \frac{\sqrt{2}}{8 x^{2}} - \frac{\sqrt{2} \left(4 x^{2} - 1\right)}{4 x^{3}}}{\sqrt{1 - \frac{\left(4 x^{2} - 1\right)^{2}}{32 x^{4}}}}
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Segunda derivada [src] 
                      /                 /            2\\
                      |     /        2\ |    -1 + 4*x ||
                      |     \-1 + 4*x /*|4 - ---------||
      /            2\ |                 |         2   ||
  ___ |    -1 + 4*x | |                 \        x    /|
\/ 2 *|4 - ---------|*|48 - ---------------------------|
      |         2   | |           /               2\   |
      \        x    / |           |    /        2\ |   |
                      |         2 |    \-1 + 4*x / |   |
                      |        x *|1 - ------------|   |
                      |           |           4    |   |
                      \           \       32*x     /   /
--------------------------------------------------------
                         __________________             
                        /                2              
                       /      /        2\               
                2     /       \-1 + 4*x /               
            64*x *   /    1 - ------------              
                    /                4                  
                  \/             32*x
2(4−4x2−1x2)(48−(4−4x2−1x2)(4x2−1)x2(1−(4x2−1)232x4))64x21−(4x2−1)232x4\frac{\sqrt{2} \left(4 - \frac{4 x^{2} - 1}{x^{2}}\right) \left(48 - \frac{\left(4 - \frac{4 x^{2} - 1}{x^{2}}\right) \left(4 x^{2} - 1\right)}{x^{2} \left(1 - \frac{\left(4 x^{2} - 1\right)^{2}}{32 x^{4}}\right)}\right)}{64 x^{2} \sqrt{1 - \frac{\left(4 x^{2} - 1\right)^{2}}{32 x^{4}}}}
Simplificar
Tercera derivada [src] 
                      /                                        2                                 2                                \
                      |             /        2\     /        2\                 2 /            2\                  /            2\|
                      |          28*\-1 + 4*x /   5*\-1 + 4*x /      /        2\  |    -1 + 4*x |      /        2\ |    -1 + 4*x ||
                      |     32 - -------------- + --------------   3*\-1 + 4*x / *|4 - ---------|    3*\-1 + 4*x /*|4 - ---------||
      /            2\ |                 2                4                        |         2   |                  |         2   ||
  ___ |    -1 + 4*x | |                x                x                         \        x    /                  \        x    /|
\/ 2 *|4 - ---------|*|-3 - ------------------------------------ - ------------------------------- + -----------------------------|
      |         2   | |               /               2\                                       2              /               2\  |
      \        x    / |               |    /        2\ |                     /               2\               |    /        2\ |  |
                      |               |    \-1 + 4*x / |                     |    /        2\ |             2 |    \-1 + 4*x / |  |
                      |            64*|1 - ------------|                   4 |    \-1 + 4*x / |         32*x *|1 - ------------|  |
                      |               |           4    |             1024*x *|1 - ------------|               |           4    |  |
                      |               \       32*x     /                     |           4    |               \       32*x     /  |
                      \                                                      \       32*x     /                                   /
-----------------------------------------------------------------------------------------------------------------------------------
                                                              __________________                                                   
                                                             /                2                                                    
                                                            /      /        2\                                                     
                                                     3     /       \-1 + 4*x /                                                     
                                                    x *   /    1 - ------------                                                    
                                                         /                4                                                        
                                                       \/             32*x
2(4−4x2−1x2)(−3−32−28(4x2−1)x2+5(4x2−1)2x464(1−(4x2−1)232x4)+3(4−4x2−1x2)(4x2−1)32x2(1−(4x2−1)232x4)−3(4−4x2−1x2)2(4x2−1)21024x4(1−(4x2−1)232x4)2)x31−(4x2−1)232x4\frac{\sqrt{2} \left(4 - \frac{4 x^{2} - 1}{x^{2}}\right) \left(-3 - \frac{32 - \frac{28 \left(4 x^{2} - 1\right)}{x^{2}} + \frac{5 \left(4 x^{2} - 1\right)^{2}}{x^{4}}}{64 \left(1 - \frac{\left(4 x^{2} - 1\right)^{2}}{32 x^{4}}\right)} + \frac{3 \left(4 - \frac{4 x^{2} - 1}{x^{2}}\right) \left(4 x^{2} - 1\right)}{32 x^{2} \left(1 - \frac{\left(4 x^{2} - 1\right)^{2}}{32 x^{4}}\right)} - \frac{3 \left(4 - \frac{4 x^{2} - 1}{x^{2}}\right)^{2} \left(4 x^{2} - 1\right)^{2}}{1024 x^{4} \left(1 - \frac{\left(4 x^{2} - 1\right)^{2}}{32 x^{4}}\right)^{2}}\right)}{x^{3} \sqrt{1 - \frac{\left(4 x^{2} - 1\right)^{2}}{32 x^{4}}}}
Simplificar
Gráfico
Derivada de y=arccos((4x^2-1)/(sqrt(2)*4x^2))
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