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(x+x^(1/2))/arccos(3x)

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

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

Gráfico:

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Solución

Ha introducido [src]
      ___
x + \/ x 
---------
acos(3*x)
$$\frac{\sqrt{x} + x}{\operatorname{acos}{\left(3 x \right)}}$$
(x + sqrt(x))/acos(3*x)
Gráfica
Primera derivada [src]
       1                              
1 + -------                           
        ___          /      ___\      
    2*\/ x         3*\x + \/ x /      
----------- + ------------------------
 acos(3*x)       __________           
                /        2      2     
              \/  1 - 9*x  *acos (3*x)
$$\frac{1 + \frac{1}{2 \sqrt{x}}}{\operatorname{acos}{\left(3 x \right)}} + \frac{3 \left(\sqrt{x} + x\right)}{\sqrt{1 - 9 x^{2}} \operatorname{acos}^{2}{\left(3 x \right)}}$$
Segunda derivada [src]
                                       /      ___\ /            2                  3*x     \
                  /      1  \        9*\x + \/ x /*|- --------------------- + -------------|
                3*|2 + -----|                      |  /        2\                       3/2|
                  |      ___|                      |  \-1 + 9*x /*acos(3*x)   /       2\   |
    1             \    \/ x /                      \                          \1 - 9*x /   /
- ------ + ----------------------- + -------------------------------------------------------
     3/2      __________                                    acos(3*x)                       
  4*x        /        2                                                                     
           \/  1 - 9*x  *acos(3*x)                                                          
--------------------------------------------------------------------------------------------
                                         acos(3*x)                                          
$$\frac{\frac{9 \left(\sqrt{x} + x\right) \left(\frac{3 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(9 x^{2} - 1\right) \operatorname{acos}{\left(3 x \right)}}\right)}{\operatorname{acos}{\left(3 x \right)}} + \frac{3 \left(2 + \frac{1}{\sqrt{x}}\right)}{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} - \frac{1}{4 x^{\frac{3}{2}}}}{\operatorname{acos}{\left(3 x \right)}}$$
Tercera derivada [src]
  /                       /                                                   2                             \                                                                                           \
  |           /      ___\ |      1                    6                   27*x                 18*x         |                                      /      1  \ /            2                  3*x     \|
  |         9*\x + \/ x /*|------------- + ------------------------ + ------------- + ----------------------|                                    9*|2 + -----|*|- --------------------- + -------------||
  |                       |          3/2             3/2                        5/2              2          |                                      |      ___| |  /        2\                       3/2||
  |                       |/       2\      /       2\        2        /       2\      /        2\           |                                      \    \/ x / |  \-1 + 9*x /*acos(3*x)   /       2\   ||
  |  1                    \\1 - 9*x /      \1 - 9*x /   *acos (3*x)   \1 - 9*x /      \-1 + 9*x / *acos(3*x)/                 3                                \                          \1 - 9*x /   /|
3*|------ + ------------------------------------------------------------------------------------------------- - ------------------------------ + -------------------------------------------------------|
  |   5/2                                               acos(3*x)                                                         __________                                   2*acos(3*x)                      |
  |8*x                                                                                                             3/2   /        2                                                                     |
  \                                                                                                             4*x   *\/  1 - 9*x  *acos(3*x)                                                          /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                acos(3*x)                                                                                                
$$\frac{3 \left(\frac{9 \left(2 + \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(9 x^{2} - 1\right) \operatorname{acos}{\left(3 x \right)}}\right)}{2 \operatorname{acos}{\left(3 x \right)}} + \frac{9 \left(\sqrt{x} + x\right) \left(\frac{27 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + \frac{18 x}{\left(9 x^{2} - 1\right)^{2} \operatorname{acos}{\left(3 x \right)}} + \frac{1}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(3 x \right)}}\right)}{\operatorname{acos}{\left(3 x \right)}} - \frac{3}{4 x^{\frac{3}{2}} \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} + \frac{1}{8 x^{\frac{5}{2}}}\right)}{\operatorname{acos}{\left(3 x \right)}}$$
Gráfico
Derivada de (x+x^(1/2))/arccos(3x)