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arcsin(sqrt(x)/(x-5))

Derivative of arcsin(sqrt(x)/(x-5))

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

The graph:

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The solution

You have entered [src]
    /  ___\
    |\/ x |
asin|-----|
    \x - 5/
$$\operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}$$
The graph
The first derivative [src]
                     ___  
       1           \/ x   
--------------- - --------
    ___                  2
2*\/ x *(x - 5)   (x - 5) 
--------------------------
        ______________    
       /        x         
      /  1 - --------     
     /              2     
   \/        (x - 5)      
$$\frac{- \frac{\sqrt{x}}{\left(x - 5\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x - 5\right)}}{\sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
The second derivative [src]
                                                      /              ___\
                                        /      2*x  \ |    1     2*\/ x |
                                        |-1 + ------|*|- ----- + -------|
                                 ___    \     -5 + x/ |    ___    -5 + x|
    1            1           2*\/ x                   \  \/ x           /
- ------ - -------------- + --------- + ---------------------------------
     3/2     ___                    2        /        x    \         2   
  4*x      \/ x *(-5 + x)   (-5 + x)       4*|1 - ---------|*(-5 + x)    
                                             |            2|             
                                             \    (-5 + x) /             
-------------------------------------------------------------------------
                           _______________                               
                          /         x                                    
                         /  1 - --------- *(-5 + x)                      
                        /               2                                
                      \/        (-5 + x)                                 
$$\frac{\frac{2 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)}{4 \left(x - 5\right)^{2} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{1}{\sqrt{x} \left(x - 5\right)} - \frac{1}{4 x^{\frac{3}{2}}}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
The third derivative [src]
                                                                        2 /              ___\                 /              ___\                 /            ___                  \
                                                           /      2*x  \  |    1     2*\/ x |   /      3*x  \ |    1     2*\/ x |   /      2*x  \ | 1      8*\/ x           4       |
                                                         3*|-1 + ------| *|- ----- + -------|   |-2 + ------|*|- ----- + -------|   |-1 + ------|*|---- - --------- + --------------|
              ___                                          \     -5 + x/  |    ___    -5 + x|   \     -5 + x/ |    ___    -5 + x|   \     -5 + x/ | 3/2           2     ___         |
  3       6*\/ x            3                 3                           \  \/ x           /                 \  \/ x           /                 \x      (-5 + x)    \/ x *(-5 + x)/
------ - --------- + --------------- + --------------- - ------------------------------------ - --------------------------------- + -------------------------------------------------
   5/2           3     ___         2      3/2                                 2                      /        x    \         3                   /        x    \         2           
8*x      (-5 + x)    \/ x *(-5 + x)    4*x   *(-5 + x)         /        x    \          4          2*|1 - ---------|*(-5 + x)                  4*|1 - ---------|*(-5 + x)            
                                                             8*|1 - ---------| *(-5 + x)             |            2|                             |            2|                     
                                                               |            2|                       \    (-5 + x) /                             \    (-5 + x) /                     
                                                               \    (-5 + x) /                                                                                                       
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                 _______________                                                                                     
                                                                                /         x                                                                                          
                                                                               /  1 - --------- *(-5 + x)                                                                            
                                                                              /               2                                                                                      
                                                                            \/        (-5 + x)                                                                                       
$$\frac{- \frac{6 \sqrt{x}}{\left(x - 5\right)^{3}} + \frac{\left(\frac{2 x}{x - 5} - 1\right) \left(- \frac{8 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{4}{\sqrt{x} \left(x - 5\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{4 \left(x - 5\right)^{2} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{x - 5} - 2\right)}{2 \left(x - 5\right)^{3} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{3 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)^{2}}{8 \left(x - 5\right)^{4} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)^{2}} + \frac{3}{\sqrt{x} \left(x - 5\right)^{2}} + \frac{3}{4 x^{\frac{3}{2}} \left(x - 5\right)} + \frac{3}{8 x^{\frac{5}{2}}}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
3-я производная [src]
                                                                        2 /              ___\                 /              ___\                 /            ___                  \
                                                           /      2*x  \  |    1     2*\/ x |   /      3*x  \ |    1     2*\/ x |   /      2*x  \ | 1      8*\/ x           4       |
                                                         3*|-1 + ------| *|- ----- + -------|   |-2 + ------|*|- ----- + -------|   |-1 + ------|*|---- - --------- + --------------|
              ___                                          \     -5 + x/  |    ___    -5 + x|   \     -5 + x/ |    ___    -5 + x|   \     -5 + x/ | 3/2           2     ___         |
  3       6*\/ x            3                 3                           \  \/ x           /                 \  \/ x           /                 \x      (-5 + x)    \/ x *(-5 + x)/
------ - --------- + --------------- + --------------- - ------------------------------------ - --------------------------------- + -------------------------------------------------
   5/2           3     ___         2      3/2                                 2                      /        x    \         3                   /        x    \         2           
8*x      (-5 + x)    \/ x *(-5 + x)    4*x   *(-5 + x)         /        x    \          4          2*|1 - ---------|*(-5 + x)                  4*|1 - ---------|*(-5 + x)            
                                                             8*|1 - ---------| *(-5 + x)             |            2|                             |            2|                     
                                                               |            2|                       \    (-5 + x) /                             \    (-5 + x) /                     
                                                               \    (-5 + x) /                                                                                                       
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                 _______________                                                                                     
                                                                                /         x                                                                                          
                                                                               /  1 - --------- *(-5 + x)                                                                            
                                                                              /               2                                                                                      
                                                                            \/        (-5 + x)                                                                                       
$$\frac{- \frac{6 \sqrt{x}}{\left(x - 5\right)^{3}} + \frac{\left(\frac{2 x}{x - 5} - 1\right) \left(- \frac{8 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{4}{\sqrt{x} \left(x - 5\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{4 \left(x - 5\right)^{2} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{x - 5} - 2\right)}{2 \left(x - 5\right)^{3} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{3 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)^{2}}{8 \left(x - 5\right)^{4} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)^{2}} + \frac{3}{\sqrt{x} \left(x - 5\right)^{2}} + \frac{3}{4 x^{\frac{3}{2}} \left(x - 5\right)} + \frac{3}{8 x^{\frac{5}{2}}}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
The graph
Derivative of arcsin(sqrt(x)/(x-5))