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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /      1      \
acos|-------------|
    |   __________|
    |  /        2 |
    \\/  1 + 2*x  /
acos⁡(12x2+1)\operatorname{acos}{\left(\frac{1}{\sqrt{2 x^{2} + 1}} \right)} 
acos(1/(sqrt(1 + 2*x^2)))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
               2*x               
---------------------------------
     ______________           3/2
    /        1      /       2\   
   /  1 - -------- *\1 + 2*x /   
  /              2               
\/        1 + 2*x
2x1−12x2+1(2x2+1)32\frac{2 x}{\sqrt{1 - \frac{1}{2 x^{2} + 1}} \left(2 x^{2} + 1\right)^{\frac{3}{2}}}
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Segunda derivada [src] 
  /         2                   2           \
  |      6*x                 2*x            |
2*|1 - -------- - --------------------------|
  |           2                            2|
  |    1 + 2*x    /       1    \ /       2\ |
  |               |1 - --------|*\1 + 2*x / |
  |               |           2|            |
  \               \    1 + 2*x /            /
---------------------------------------------
           ______________           3/2      
          /        1      /       2\         
         /  1 - -------- *\1 + 2*x /         
        /              2                     
      \/        1 + 2*x
2(−6x22x2+1−2x2(1−12x2+1)(2x2+1)2+1)1−12x2+1(2x2+1)32\frac{2 \left(- \frac{6 x^{2}}{2 x^{2} + 1} - \frac{2 x^{2}}{\left(1 - \frac{1}{2 x^{2} + 1}\right) \left(2 x^{2} + 1\right)^{2}} + 1\right)}{\sqrt{1 - \frac{1}{2 x^{2} + 1}} \left(2 x^{2} + 1\right)^{\frac{3}{2}}}
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Tercera derivada [src] 
    /                                      2                    2                            2           \
    |                 3                30*x                  6*x                         20*x            |
4*x*|-9 - ------------------------- + -------- + --------------------------- + --------------------------|
    |     /       1    \ /       2\          2                 2           3                            2|
    |     |1 - --------|*\1 + 2*x /   1 + 2*x    /       1    \  /       2\    /       1    \ /       2\ |
    |     |           2|                         |1 - --------| *\1 + 2*x /    |1 - --------|*\1 + 2*x / |
    |     \    1 + 2*x /                         |           2|                |           2|            |
    \                                            \    1 + 2*x /                \    1 + 2*x /            /
----------------------------------------------------------------------------------------------------------
                                         ______________           5/2                                     
                                        /        1      /       2\                                        
                                       /  1 - -------- *\1 + 2*x /                                        
                                      /              2                                                    
                                    \/        1 + 2*x
4x(30x22x2+1+20x2(1−12x2+1)(2x2+1)2+6x2(1−12x2+1)2(2x2+1)3−9−3(1−12x2+1)(2x2+1))1−12x2+1(2x2+1)52\frac{4 x \left(\frac{30 x^{2}}{2 x^{2} + 1} + \frac{20 x^{2}}{\left(1 - \frac{1}{2 x^{2} + 1}\right) \left(2 x^{2} + 1\right)^{2}} + \frac{6 x^{2}}{\left(1 - \frac{1}{2 x^{2} + 1}\right)^{2} \left(2 x^{2} + 1\right)^{3}} - 9 - \frac{3}{\left(1 - \frac{1}{2 x^{2} + 1}\right) \left(2 x^{2} + 1\right)}\right)}{\sqrt{1 - \frac{1}{2 x^{2} + 1}} \left(2 x^{2} + 1\right)^{\frac{5}{2}}}
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Gráfico
Derivada de y=arccos(1/sqrt(1+2x^2))
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