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log4(x-1)*arcsinx^4

Derivative of log4(x-1)*arcsinx^4

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

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The solution

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               4   
log(x - 1)*asin (x)
-------------------
       log(4)      
$$\frac{\log{\left(x - 1 \right)} \operatorname{asin}^{4}{\left(x \right)}}{\log{\left(4 \right)}}$$
  /               4   \
d |log(x - 1)*asin (x)|
--|-------------------|
dx\       log(4)      /
$$\frac{d}{d x} \frac{\log{\left(x - 1 \right)} \operatorname{asin}^{4}{\left(x \right)}}{\log{\left(4 \right)}}$$
The graph
The first derivative [src]
       4               3              
   asin (x)      4*asin (x)*log(x - 1)
-------------- + ---------------------
(x - 1)*log(4)        ________        
                     /      2         
                   \/  1 - x  *log(4) 
$$\frac{\operatorname{asin}^{4}{\left(x \right)}}{\left(x - 1\right) \log{\left(4 \right)}} + \frac{4 \log{\left(x - 1 \right)} \operatorname{asin}^{3}{\left(x \right)}}{\sqrt{- x^{2} + 1} \log{\left(4 \right)}}$$
The second derivative [src]
         /       2                                                                    \
    2    |   asin (x)     /     3       x*asin(x) \                    8*asin(x)      |
asin (x)*|- --------- + 4*|- ------- + -----------|*log(-1 + x) + --------------------|
         |          2     |        2           3/2|                  ________         |
         |  (-1 + x)      |  -1 + x    /     2\   |                 /      2          |
         \                \            \1 - x /   /               \/  1 - x  *(-1 + x)/
---------------------------------------------------------------------------------------
                                         log(4)                                        
$$\frac{\left(4 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{3}{x^{2} - 1}\right) \log{\left(x - 1 \right)} - \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(x - 1\right)^{2}} + \frac{8 \operatorname{asin}{\left(x \right)}}{\sqrt{- x^{2} + 1} \left(x - 1\right)}\right) \operatorname{asin}^{2}{\left(x \right)}}{\log{\left(4 \right)}}$$
The third derivative [src]
  /                                                                                                                /     3       x*asin(x) \        \        
  |                                                                                                              6*|- ------- + -----------|*asin(x)|        
  |                                                                                                                |        2           3/2|        |        
  |     3        /                    2          2     2                 \                           2             |  -1 + x    /     2\   |        |        
  | asin (x)     |     6          asin (x)    3*x *asin (x)   9*x*asin(x)|                     6*asin (x)          \            \1 - x /   /        |        
2*|--------- + 2*|----------- + ----------- + ------------- + -----------|*log(-1 + x) - --------------------- + -----------------------------------|*asin(x)
  |        3     |        3/2           3/2            5/2              2|                  ________                            -1 + x              |        
  |(-1 + x)      |/     2\      /     2\       /     2\        /      2\ |                 /      2          2                                      |        
  \              \\1 - x /      \1 - x /       \1 - x /        \-1 + x / /               \/  1 - x  *(-1 + x)                                       /        
-------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                            log(4)                                                                           
$$\frac{2 \cdot \left(2 \cdot \left(\frac{9 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left(x - 1 \right)} + \frac{6 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{3}{x^{2} - 1}\right) \operatorname{asin}{\left(x \right)}}{x - 1} + \frac{\operatorname{asin}^{3}{\left(x \right)}}{\left(x - 1\right)^{3}} - \frac{6 \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{- x^{2} + 1} \left(x - 1\right)^{2}}\right) \operatorname{asin}{\left(x \right)}}{\log{\left(4 \right)}}$$
The graph
Derivative of log4(x-1)*arcsinx^4