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log(3)*arcsin(sqrt(x)/(x-5))
The derivative of the function/ log(3)*arcsin(sqrt(x)/(x-5))

Derivative of log(3)*arcsin(sqrt(x)/(x-5))

Function f() - derivative -N order at the point
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You have entered [src] 
           /  ___\
           |\/ x |
log(3)*asin|-----|
           \x - 5/
log⁡(3)asin⁡(xx−5)\log{\left(3 \right)} \operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}
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The graph
02468-8-6-4-2-10105-5
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The first derivative [src] 
/                     ___  \       
|       1           \/ x   |       
|--------------- - --------|*log(3)
|    ___                  2|       
\2*\/ x *(x - 5)   (x - 5) /       
-----------------------------------
             ______________        
            /        x             
           /  1 - --------         
          /              2         
        \/        (x - 5)
(−x(x−5)2+12x(x−5))log⁡(3)−x(x−5)2+1\frac{\left(- \frac{\sqrt{x}}{\left(x - 5\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x - 5\right)}\right) \log{\left(3 \right)}}{\sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}
Simplify
The second derivative [src] 
 /                                                    /              ___\\        
 |                                      /      2*x  \ |    1     2*\/ x ||        
 |                                      |-1 + ------|*|- ----- + -------||        
 |                               ___    \     -5 + x/ |    ___    -5 + x||        
 |  1            1           2*\/ x                   \  \/ x           /|        
-|------ + -------------- - --------- + ---------------------------------|*log(3) 
 |   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)
−(−2x(x−5)2+(2xx−5−1x)(2xx−5−1)4(x−5)2(x(x−5)2−1)+1x(x−5)+14x32)log⁡(3)(x−5)−x(x−5)2+1- \frac{\left(- \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}}}\right) \log{\left(3 \right)}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}
Simplify
The third derivative [src] 
/                                                                       /              ___\                  2 /              ___\                 /            ___                  \\       
|                                                         /      3*x  \ |    1     2*\/ x |     /      2*x  \  |    1     2*\/ x |   /      2*x  \ | 1      8*\/ x           4       ||       
|                                                         |-2 + ------|*|- ----- + -------|   3*|-1 + ------| *|- ----- + -------|   |-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)/|       
|------ - --------- + --------------- + --------------- + --------------------------------- - ------------------------------------ - -------------------------------------------------|*log(3)
|   5/2           3     ___         2      3/2                 /         x    \         3                          2                              /         x    \         2          |       
|8*x      (-5 + x)    \/ x *(-5 + x)    4*x   *(-5 + x)      2*|-1 + ---------|*(-5 + x)           /         x    \          4                  4*|-1 + ---------|*(-5 + x)           |       
|                                                              |             2|                  8*|-1 + ---------| *(-5 + x)                     |             2|                    |       
|                                                              \     (-5 + x) /                    |             2|                               \     (-5 + x) /                    |       
\                                                                                                  \     (-5 + x) /                                                                   /       
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                     _______________                                                                                          
                                                                                    /         x                                                                                               
                                                                                   /  1 - --------- *(-5 + x)                                                                                 
                                                                                  /               2                                                                                           
                                                                                \/        (-5 + x)
(−6x(x−5)3−(2xx−5−1)(−8x(x−5)2+4x(x−5)+1x32)4(x−5)2(x(x−5)2−1)+(2xx−5−1x)(3xx−5−2)2(x−5)3(x(x−5)2−1)−3(2xx−5−1x)(2xx−5−1)28(x−5)4(x(x−5)2−1)2+3x(x−5)2+34x32(x−5)+38x52)log⁡(3)(x−5)−x(x−5)2+1\frac{\left(- \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}}}\right) \log{\left(3 \right)}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}
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The graph
Derivative of log(3)*arcsin(sqrt(x)/(x-5))
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