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(x+sqrt(sqrt(x)))/arccos(3*x)
Derivada de la función/ (x+sqrt(sqrt(x)))/arccos(3*x)

Derivada de (x+sqrt(sqrt(x)))/arccos(3*x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
       _______
      /   ___ 
x + \/  \/ x  
--------------
  acos(3*x)
x+xacos⁡(3x)\frac{\sqrt{\sqrt{x}} + x}{\operatorname{acos}{\left(3 x \right)}} 
(x + sqrt(sqrt(x)))/acos(3*x)
Gráfica
02468-8-6-4-2-1010050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    4 ___                           
    \/ x         /       _______\   
1 + -----        |      /   ___ |   
     4*x       3*\x + \/  \/ x  /   
--------- + ------------------------
acos(3*x)      __________           
              /        2      2     
            \/  1 - 9*x  *acos (3*x)
x44x+1acos⁡(3x)+3(x+x)1−9x2acos⁡2(3x)\frac{\frac{\sqrt[4]{x}}{4 x} + 1}{\operatorname{acos}{\left(3 x \right)}} + \frac{3 \left(\sqrt{\sqrt{x}} + x\right)}{\sqrt{1 - 9 x^{2}} \operatorname{acos}^{2}{\left(3 x \right)}}
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Segunda derivada [src] 
  /                                          /    4 ___\ /            2                  3*x     \\
  |                          1             3*\x + \/ x /*|- --------------------- + -------------||
  |                     4 + ----                         |  /        2\                       3/2||
  |                          3/4                         |  \-1 + 9*x /*acos(3*x)   /       2\   ||
  |     1                   x                            \                          \1 - 9*x /   /|
3*|- ------- + ------------------------- + -------------------------------------------------------|
  |      7/4        __________                                    acos(3*x)                       |
  |  16*x          /        2                                                                     |
  \            2*\/  1 - 9*x  *acos(3*x)                                                          /
---------------------------------------------------------------------------------------------------
                                             acos(3*x)
3(3(x4+x)(3x(1−9x2)32−2(9x2−1)acos⁡(3x))acos⁡(3x)+4+1x3421−9x2acos⁡(3x)−116x74)acos⁡(3x)\frac{3 \left(\frac{3 \left(\sqrt[4]{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{4 + \frac{1}{x^{\frac{3}{4}}}}{2 \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} - \frac{1}{16 x^{\frac{7}{4}}}\right)}{\operatorname{acos}{\left(3 x \right)}}
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Tercera derivada [src] 
  /                         /                                                   2                             \                                                                                           \
  |             /    4 ___\ |      1                    6                   27*x                 18*x         |                                       /     1  \ /            2                  3*x     \|
  |           9*\x + \/ x /*|------------- + ------------------------ + ------------- + ----------------------|                                     9*|4 + ----|*|- --------------------- + -------------||
  |                         |          3/2             3/2                        5/2              2          |                                       |     3/4| |  /        2\                       3/2||
  |                         |/       2\      /       2\        2        /       2\      /        2\           |                                       \    x   / |  \-1 + 9*x /*acos(3*x)   /       2\   ||
  |   7                     \\1 - 9*x /      \1 - 9*x /   *acos (3*x)   \1 - 9*x /      \-1 + 9*x / *acos(3*x)/                  9                               \                          \1 - 9*x /   /|
3*|-------- + ------------------------------------------------------------------------------------------------- - ------------------------------- + ------------------------------------------------------|
  |    11/4                                               acos(3*x)                                                          __________                                  4*acos(3*x)                      |
  |64*x                                                                                                               7/4   /        2                                                                    |
  \                                                                                                               16*x   *\/  1 - 9*x  *acos(3*x)                                                         /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 acos(3*x)
3(9(4+1x34)(3x(1−9x2)32−2(9x2−1)acos⁡(3x))4acos⁡(3x)+9(x4+x)(27x2(1−9x2)52+18x(9x2−1)2acos⁡(3x)+1(1−9x2)32+6(1−9x2)32acos⁡2(3x))acos⁡(3x)−916x741−9x2acos⁡(3x)+764x114)acos⁡(3x)\frac{3 \left(\frac{9 \left(4 + \frac{1}{x^{\frac{3}{4}}}\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)}{4 \operatorname{acos}{\left(3 x \right)}} + \frac{9 \left(\sqrt[4]{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{9}{16 x^{\frac{7}{4}} \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} + \frac{7}{64 x^{\frac{11}{4}}}\right)}{\operatorname{acos}{\left(3 x \right)}}
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Gráfico
Derivada de (x+sqrt(sqrt(x)))/arccos(3*x)
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