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Derivada de arcsin(4/(3x))*(log(2,sqrt(5x3)))

Función f() - derivada -er orden en el punto
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Solución

Ha introducido [src]
    / 4 \    /     ______\
asin|---|*log\2, \/ 5*x3 /
    \3*x/                 
$$\log{\left(2 \right)} \operatorname{asin}{\left(\frac{4}{3 x} \right)}$$
asin(4/((3*x)))*log(2, sqrt(5*x3))
Primera derivada [src]
      /     ______\ 
-4*log\2, \/ 5*x3 / 
--------------------
          __________
   2     /      16  
3*x *   /  1 - ---- 
       /          2 
     \/        9*x  
$$- \frac{4 \log{\left(2 \right)}}{3 x^{2} \sqrt{1 - \frac{16}{9 x^{2}}}}$$
Segunda derivada [src]
  /         8     \    /     ______\
8*|1 + -----------|*log\2, \/ 5*x3 /
  |     2 /    16\|                 
  |    x *|9 - --||                 
  |       |     2||                 
  \       \    x //                 
------------------------------------
                  __________        
           3     /      16          
        3*x *   /  1 - ----         
               /          2         
             \/        9*x          
$$\frac{8 \left(1 + \frac{8}{x^{2} \left(9 - \frac{16}{x^{2}}\right)}\right) \log{\left(2 \right)}}{3 x^{3} \sqrt{1 - \frac{16}{9 x^{2}}}}$$
Tercera derivada [src]
   /        128              56     \    /     ______\
-8*|1 + ------------ + -------------|*log\2, \/ 5*x3 /
   |               2      2 /    16\|                 
   |     4 /    16\    3*x *|9 - --||                 
   |    x *|9 - --|         |     2||                 
   |       |     2|         \    x /|                 
   \       \    x /                 /                 
------------------------------------------------------
                          __________                  
                   4     /      16                    
                  x *   /  1 - ----                   
                       /          2                   
                     \/        9*x                    
$$- \frac{8 \left(1 + \frac{56}{3 x^{2} \left(9 - \frac{16}{x^{2}}\right)} + \frac{128}{x^{4} \left(9 - \frac{16}{x^{2}}\right)^{2}}\right) \log{\left(2 \right)}}{x^{4} \sqrt{1 - \frac{16}{9 x^{2}}}}$$