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ln(arccos*(1/sqrtx))

Derivative of ln(arccos*(1/sqrtx))

Function f() - derivative -N order at the point
v

The graph:

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The solution

You have entered [src]
   /    /    1  \\
log|acos|1*-----||
   |    |    ___||
   \    \  \/ x //
$$\log{\left(\operatorname{acos}{\left(1 \cdot \frac{1}{\sqrt{x}} \right)} \right)}$$
d /   /    /    1  \\\
--|log|acos|1*-----|||
dx|   |    |    ___|||
  \   \    \  \/ x ///
$$\frac{d}{d x} \log{\left(\operatorname{acos}{\left(1 \cdot \frac{1}{\sqrt{x}} \right)} \right)}$$
The graph
The first derivative [src]
               1                
--------------------------------
           _______              
   3/2    /     1      /    1  \
2*x   *  /  1 - - *acos|1*-----|
       \/       x      |    ___|
                       \  \/ x /
$$\frac{1}{2 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x}} \operatorname{acos}{\left(1 \cdot \frac{1}{\sqrt{x}} \right)}}$$
The second derivative [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 /                         
$$- \frac{\frac{1}{x^{3} \cdot \left(1 - \frac{1}{x}\right) \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{3}{x^{\frac{5}{2}} \sqrt{1 - \frac{1}{x}}} + \frac{1}{x^{\frac{7}{2}} \left(1 - \frac{1}{x}\right)^{\frac{3}{2}}}}{4 \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}}$$
The third derivative [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 /                                                             
$$\frac{\frac{9}{x^{4} \cdot \left(1 - \frac{1}{x}\right) \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{3}{x^{5} \left(1 - \frac{1}{x}\right)^{2} \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{15}{x^{\frac{7}{2}} \sqrt{1 - \frac{1}{x}}} + \frac{10}{x^{\frac{9}{2}} \left(1 - \frac{1}{x}\right)^{\frac{3}{2}}} + \frac{2}{x^{\frac{9}{2}} \left(1 - \frac{1}{x}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{3}{x^{\frac{11}{2}} \left(1 - \frac{1}{x}\right)^{\frac{5}{2}}}}{8 \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}}$$
The graph
Derivative of ln(arccos*(1/sqrtx))