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x*log(x,2)/arcsin(3*x)

Derivada de x*log(x,2)/arcsin(3*x)

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Solución

Ha introducido [src]
   log(x)
 x*------
   log(2)
---------
asin(3*x)
$$\frac{x \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}}{\operatorname{asin}{\left(3 x \right)}}$$
(x*(log(x)/log(2)))/asin(3*x)
Gráfica
Primera derivada [src]
  1      log(x)                                  
------ + ------                                  
log(2)   log(2)              3*x*log(x)          
--------------- - -------------------------------
   asin(3*x)         __________                  
                    /        2      2            
                  \/  1 - 9*x  *asin (3*x)*log(2)
$$- \frac{3 x \log{\left(x \right)}}{\sqrt{1 - 9 x^{2}} \log{\left(2 \right)} \operatorname{asin}^{2}{\left(3 x \right)}} + \frac{\frac{\log{\left(x \right)}}{\log{\left(2 \right)}} + \frac{1}{\log{\left(2 \right)}}}{\operatorname{asin}{\left(3 x \right)}}$$
Segunda derivada [src]
                                  /          2                  3*x     \       
                              9*x*|--------------------- + -------------|*log(x)
                                  |/        2\                       3/2|       
                                  |\-1 + 9*x /*asin(3*x)   /       2\   |       
1        6*(1 + log(x))           \                        \1 - 9*x /   /       
- - ----------------------- - --------------------------------------------------
x      __________                                 asin(3*x)                     
      /        2                                                                
    \/  1 - 9*x  *asin(3*x)                                                     
--------------------------------------------------------------------------------
                                asin(3*x)*log(2)                                
$$\frac{- \frac{9 x \left(\frac{3 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(9 x^{2} - 1\right) \operatorname{asin}{\left(3 x \right)}}\right) \log{\left(x \right)}}{\operatorname{asin}{\left(3 x \right)}} - \frac{6 \left(\log{\left(x \right)} + 1\right)}{\sqrt{1 - 9 x^{2}} \operatorname{asin}{\left(3 x \right)}} + \frac{1}{x}}{\log{\left(2 \right)} \operatorname{asin}{\left(3 x \right)}}$$
Tercera derivada [src]
 /                                                                                                /                                                   2                             \       \ 
 |                                                 /          2                  3*x     \        |      1                    6                   27*x                 18*x         |       | 
 |                                 27*(1 + log(x))*|--------------------- + -------------|   27*x*|------------- + ------------------------ + ------------- - ----------------------|*log(x)| 
 |                                                 |/        2\                       3/2|        |          3/2             3/2                        5/2              2          |       | 
 |                                                 |\-1 + 9*x /*asin(3*x)   /       2\   |        |/       2\      /       2\        2        /       2\      /        2\           |       | 
 |1                9                               \                        \1 - 9*x /   /        \\1 - 9*x /      \1 - 9*x /   *asin (3*x)   \1 - 9*x /      \-1 + 9*x / *asin(3*x)/       | 
-|-- + ------------------------- + ------------------------------------------------------- + -----------------------------------------------------------------------------------------------| 
 | 2        __________                                    asin(3*x)                                                                     asin(3*x)                                           | 
 |x        /        2                                                                                                                                                                       | 
 \     x*\/  1 - 9*x  *asin(3*x)                                                                                                                                                            / 
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                       asin(3*x)*log(2)                                                                                       
$$- \frac{\frac{27 x \left(\frac{27 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} - \frac{18 x}{\left(9 x^{2} - 1\right)^{2} \operatorname{asin}{\left(3 x \right)}} + \frac{1}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(3 x \right)}}\right) \log{\left(x \right)}}{\operatorname{asin}{\left(3 x \right)}} + \frac{27 \left(\frac{3 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(9 x^{2} - 1\right) \operatorname{asin}{\left(3 x \right)}}\right) \left(\log{\left(x \right)} + 1\right)}{\operatorname{asin}{\left(3 x \right)}} + \frac{9}{x \sqrt{1 - 9 x^{2}} \operatorname{asin}{\left(3 x \right)}} + \frac{1}{x^{2}}}{\log{\left(2 \right)} \operatorname{asin}{\left(3 x \right)}}$$
Gráfico
Derivada de x*log(x,2)/arcsin(3*x)