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(x+√√x)/arccos(3x)
Derivada de la función/ arccos/ cos(3x)/ (x+√√x)/arccos(3x)

Derivada de (x+√√x)/arccos(3x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
      _____
x + \/ 4*x 
-----------
 acos(3*x)
4x+xacos⁡(3x)\frac{\sqrt{4 x} + x}{\operatorname{acos}{\left(3 x \right)}} 
(x + sqrt(4*x))/acos(3*x)
Gráfica
02468-8-6-4-2-10100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        ___                           
    2*\/ x                            
1 + -------         /      _____\     
      2*x         3*\x + \/ 4*x /     
----------- + ------------------------
 acos(3*x)       __________           
                /        2      2     
              \/  1 - 9*x  *acos (3*x)
2x2x+1acos⁡(3x)+3(4x+x)1−9x2acos⁡2(3x)\frac{\frac{2 \sqrt{x}}{2 x} + 1}{\operatorname{acos}{\left(3 x \right)}} + \frac{3 \left(\sqrt{4 x} + x\right)}{\sqrt{1 - 9 x^{2}} \operatorname{acos}^{2}{\left(3 x \right)}}
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Segunda derivada [src] 
                                       /        ___\ /            2                  3*x     \
                  /      1  \        9*\x + 2*\/ x /*|- --------------------- + -------------|
                6*|1 + -----|                        |  /        2\                       3/2|
                  |      ___|                        |  \-1 + 9*x /*acos(3*x)   /       2\   |
    1             \    \/ x /                        \                          \1 - 9*x /   /
- ------ + ----------------------- + ---------------------------------------------------------
     3/2      __________                                     acos(3*x)                        
  2*x        /        2                                                                       
           \/  1 - 9*x  *acos(3*x)                                                            
----------------------------------------------------------------------------------------------
                                          acos(3*x)
6(1+1x)1−9x2acos⁡(3x)+9(2x+x)(3x(1−9x2)32−2(9x2−1)acos⁡(3x))acos⁡(3x)−12x32acos⁡(3x)\frac{\frac{6 \left(1 + \frac{1}{\sqrt{x}}\right)}{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} + \frac{9 \left(2 \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{1}{2 x^{\frac{3}{2}}}}{\operatorname{acos}{\left(3 x \right)}}
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Tercera derivada [src] 
  /                                                                                   /                                                   2                             \                                 \
  |           /      1  \ /            2                  3*x     \     /        ___\ |      1                    6                   27*x                 18*x         |                                 |
  |         9*|1 + -----|*|- --------------------- + -------------|   9*\x + 2*\/ x /*|------------- + ------------------------ + ------------- + ----------------------|                                 |
  |           |      ___| |  /        2\                       3/2|                   |          3/2             3/2                        5/2              2          |                                 |
  |           \    \/ x / |  \-1 + 9*x /*acos(3*x)   /       2\   |                   |/       2\      /       2\        2        /       2\      /        2\           |                                 |
  |  1                    \                          \1 - 9*x /   /                   \\1 - 9*x /      \1 - 9*x /   *acos (3*x)   \1 - 9*x /      \-1 + 9*x / *acos(3*x)/                 3               |
3*|------ + ------------------------------------------------------- + --------------------------------------------------------------------------------------------------- - ------------------------------|
  |   5/2                          acos(3*x)                                                                       acos(3*x)                                                          __________          |
  |4*x                                                                                                                                                                         3/2   /        2           |
  \                                                                                                                                                                         2*x   *\/  1 - 9*x  *acos(3*x)/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 acos(3*x)
3(9(1+1x)(3x(1−9x2)32−2(9x2−1)acos⁡(3x))acos⁡(3x)+9(2x+x)(27x2(1−9x2)52+18x(9x2−1)2acos⁡(3x)+1(1−9x2)32+6(1−9x2)32acos⁡2(3x))acos⁡(3x)−32x321−9x2acos⁡(3x)+14x52)acos⁡(3x)\frac{3 \left(\frac{9 \left(1 + \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)}{\operatorname{acos}{\left(3 x \right)}} + \frac{9 \left(2 \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}{2 x^{\frac{3}{2}} \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} + \frac{1}{4 x^{\frac{5}{2}}}\right)}{\operatorname{acos}{\left(3 x \right)}}
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Gráfico
Derivada de (x+√√x)/arccos(3x)
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