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log(acos(1/sqrt(x)))
Derivada de la función/ sqrt(x)/ log(acos(1/sqrt(x)))

Derivada de log(acos(1/sqrt(x)))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
   /    /  1  \\
log|acos|-----||
   |    |  ___||
   \    \\/ x //
log⁡(acos⁡(1x))\log{\left(\operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)} \right)} 
log(acos(1/(sqrt(x))))
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
              1               
------------------------------
           _______            
   3/2    /     1      /  1  \
2*x   *  /  1 - - *acos|-----|
       \/       x      |  ___|
                       \\/ x /
12x321−1xacos⁡(1x)\frac{1}{2 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x}} \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}}
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Segunda derivada [src] 
 /       1                 3                     1           \ 
-|--------------- + ---------------- + ----------------------| 
 |            3/2            _______    3 /    1\     /  1  \| 
 | 7/2 /    1\       5/2    /     1    x *|1 - -|*acos|-----|| 
 |x   *|1 - -|      x   *  /  1 - -       \    x/     |  ___|| 
 \     \    x/           \/       x                   \\/ x // 
---------------------------------------------------------------
                               /  1  \                         
                         4*acos|-----|                         
                               |  ___|                         
                               \\/ x /
−1x3(1−1x)acos⁡(1x)+3x521−1x+1x72(1−1x)324acos⁡(1x)- \frac{\frac{1}{x^{3} \left(1 - \frac{1}{x}\right) \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{3}{x^{\frac{5}{2}} \sqrt{1 - \frac{1}{x}}} + \frac{1}{x^{\frac{7}{2}} \left(1 - \frac{1}{x}\right)^{\frac{3}{2}}}}{4 \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}}
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Tercera derivada [src] 
       3                  10                15                       2                            3                        9           
---------------- + --------------- + ---------------- + ---------------------------- + ----------------------- + ----------------------
             5/2               3/2            _______               3/2                          2                4 /    1\     /  1  \
 11/2 /    1\       9/2 /    1\       7/2    /     1     9/2 /    1\        2/  1  \    5 /    1\      /  1  \   x *|1 - -|*acos|-----|
x    *|1 - -|      x   *|1 - -|      x   *  /  1 - -    x   *|1 - -|   *acos |-----|   x *|1 - -| *acos|-----|      \    x/     |  ___|
      \    x/           \    x/           \/       x         \    x/         |  ___|      \    x/      |  ___|                  \\/ x /
                                                                             \\/ x /                   \\/ x /                         
---------------------------------------------------------------------------------------------------------------------------------------
                                                                   /  1  \                                                             
                                                             8*acos|-----|                                                             
                                                                   |  ___|                                                             
                                                                   \\/ x /
9x4(1−1x)acos⁡(1x)+3x5(1−1x)2acos⁡(1x)+15x721−1x+10x92(1−1x)32+2x92(1−1x)32acos⁡2(1x)+3x112(1−1x)528acos⁡(1x)\frac{\frac{9}{x^{4} \left(1 - \frac{1}{x}\right) \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{3}{x^{5} \left(1 - \frac{1}{x}\right)^{2} \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{15}{x^{\frac{7}{2}} \sqrt{1 - \frac{1}{x}}} + \frac{10}{x^{\frac{9}{2}} \left(1 - \frac{1}{x}\right)^{\frac{3}{2}}} + \frac{2}{x^{\frac{9}{2}} \left(1 - \frac{1}{x}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{3}{x^{\frac{11}{2}} \left(1 - \frac{1}{x}\right)^{\frac{5}{2}}}}{8 \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}}
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Gráfico
Derivada de log(acos(1/sqrt(x)))
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