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Derivative of 15*arcsin((x-1)/x)

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

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The solution

You have entered [src]
       /x - 1\
15*asin|-----|
       \  x  /
$$15 \operatorname{asin}{\left(\frac{x - 1}{x} \right)}$$
15*asin((x - 1)/x)
The graph
The first derivative [src]
      /1   x - 1\   
   15*|- - -----|   
      |x      2 |   
      \      x  /   
--------------------
      ______________
     /            2 
    /      (x - 1)  
   /   1 - -------- 
  /            2    
\/            x     
$$\frac{15 \left(\frac{1}{x} - \frac{x - 1}{x^{2}}\right)}{\sqrt{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}}}$$
The second derivative [src]
                 /    /    -1 + x\         \
                 |    |1 - ------|*(-1 + x)|
    /    -1 + x\ |    \      x   /         |
-15*|1 - ------|*|2 - ---------------------|
    \      x   / |        /            2\  |
                 |        |    (-1 + x) |  |
                 |      x*|1 - ---------|  |
                 |        |         2   |  |
                 \        \        x    /  /
--------------------------------------------
                   _______________          
                  /             2           
           2     /      (-1 + x)            
          x *   /   1 - ---------           
               /             2              
             \/             x               
$$- \frac{15 \left(1 - \frac{x - 1}{x}\right) \left(2 - \frac{\left(1 - \frac{x - 1}{x}\right) \left(x - 1\right)}{x \left(1 - \frac{\left(x - 1\right)^{2}}{x^{2}}\right)}\right)}{x^{2} \sqrt{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}}}$$
The third derivative [src]
                /                               2                                                      \
                |        4*(-1 + x)   3*(-1 + x)                                            2          |
                |    1 - ---------- + -----------     /    -1 + x\              /    -1 + x\          2|
                |            x              2       4*|1 - ------|*(-1 + x)   3*|1 - ------| *(-1 + x) |
   /    -1 + x\ |                          x          \      x   /              \      x   /           |
15*|1 - ------|*|6 + ---------------------------- - ----------------------- + -------------------------|
   \      x   / |                       2                /            2\                           2   |
                |               (-1 + x)                 |    (-1 + x) |            /            2\    |
                |           1 - ---------              x*|1 - ---------|          2 |    (-1 + x) |    |
                |                    2                   |         2   |         x *|1 - ---------|    |
                |                   x                    \        x    /            |         2   |    |
                \                                                                   \        x    /    /
--------------------------------------------------------------------------------------------------------
                                                 _______________                                        
                                                /             2                                         
                                         3     /      (-1 + x)                                          
                                        x *   /   1 - ---------                                         
                                             /             2                                            
                                           \/             x                                             
$$\frac{15 \left(1 - \frac{x - 1}{x}\right) \left(6 + \frac{1 - \frac{4 \left(x - 1\right)}{x} + \frac{3 \left(x - 1\right)^{2}}{x^{2}}}{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}} - \frac{4 \left(1 - \frac{x - 1}{x}\right) \left(x - 1\right)}{x \left(1 - \frac{\left(x - 1\right)^{2}}{x^{2}}\right)} + \frac{3 \left(1 - \frac{x - 1}{x}\right)^{2} \left(x - 1\right)^{2}}{x^{2} \left(1 - \frac{\left(x - 1\right)^{2}}{x^{2}}\right)^{2}}\right)}{x^{3} \sqrt{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}}}$$