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y=th^3(2x+2)/arcsin(5x)
Derivada de la función/ arcsin/ sin(5x)/ y=th^3(2x+2)/arcsin(5x)

Derivada de y=th^3(2x+2)/arcsin(5x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    3         
tanh (2*x + 2)
--------------
  asin(5*x)
tanh⁡3(2x+2)asin⁡(5x)\frac{\tanh^{3}{\left(2 x + 2 \right)}}{\operatorname{asin}{\left(5 x \right)}} 
tanh(2*x + 2)^3/asin(5*x)
Gráfica
02468-8-6-4-2-1010-2020
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    2          /          2         \              3             
tanh (2*x + 2)*\6 - 6*tanh (2*x + 2)/        5*tanh (2*x + 2)    
------------------------------------- - -------------------------
              asin(5*x)                    ___________           
                                          /         2      2     
                                        \/  1 - 25*x  *asin (5*x)
(6−6tanh⁡2(2x+2))tanh⁡2(2x+2)asin⁡(5x)−5tanh⁡3(2x+2)1−25x2asin⁡2(5x)\frac{\left(6 - 6 \tanh^{2}{\left(2 x + 2 \right)}\right) \tanh^{2}{\left(2 x + 2 \right)}}{\operatorname{asin}{\left(5 x \right)}} - \frac{5 \tanh^{3}{\left(2 x + 2 \right)}}{\sqrt{1 - 25 x^{2}} \operatorname{asin}^{2}{\left(5 x \right)}}
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Segunda derivada [src] 
/                                                              2            /          2                   5*x      \                                             \                
|                                                       25*tanh (2*(1 + x))*|---------------------- + --------------|                                             |                
|                                                                           |/         2\                        3/2|                                             |                
|                                                                           |\-1 + 25*x /*asin(5*x)   /        2\   |      /         2           \                |                
|   /         2           \ /           2           \                       \                         \1 - 25*x /   /   60*\-1 + tanh (2*(1 + x))/*tanh(2*(1 + x))|                
|24*\-1 + tanh (2*(1 + x))/*\-1 + 2*tanh (2*(1 + x))/ - ------------------------------------------------------------- + ------------------------------------------|*tanh(2*(1 + x))
|                                                                                 asin(5*x)                                         ___________                   |                
|                                                                                                                                  /         2                    |                
\                                                                                                                                \/  1 - 25*x  *asin(5*x)         /                
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                                                                                     asin(5*x)
(−25(5x(1−25x2)32+2(25x2−1)asin⁡(5x))tanh⁡2(2(x+1))asin⁡(5x)+24(tanh⁡2(2(x+1))−1)(2tanh⁡2(2(x+1))−1)+60(tanh⁡2(2(x+1))−1)tanh⁡(2(x+1))1−25x2asin⁡(5x))tanh⁡(2(x+1))asin⁡(5x)\frac{\left(- \frac{25 \left(\frac{5 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(25 x^{2} - 1\right) \operatorname{asin}{\left(5 x \right)}}\right) \tanh^{2}{\left(2 \left(x + 1\right) \right)}}{\operatorname{asin}{\left(5 x \right)}} + 24 \left(\tanh^{2}{\left(2 \left(x + 1\right) \right)} - 1\right) \left(2 \tanh^{2}{\left(2 \left(x + 1\right) \right)} - 1\right) + \frac{60 \left(\tanh^{2}{\left(2 \left(x + 1\right) \right)} - 1\right) \tanh{\left(2 \left(x + 1\right) \right)}}{\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}}\right) \tanh{\left(2 \left(x + 1\right) \right)}}{\operatorname{asin}{\left(5 x \right)}}
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Tercera derivada [src] 
                                                                                                                                                 /                                                     2                               \                                                                                                                                                                 
                                                                                                                                    3            |      1                      6                   75*x                   30*x         |           2            /         2           \ /          2                   5*x      \                                                                        
                                                                                                                            125*tanh (2*(1 + x))*|-------------- + ------------------------- + -------------- - -----------------------|   450*tanh (2*(1 + x))*\-1 + tanh (2*(1 + x))/*|---------------------- + --------------|                                                                        
                                                                                                                                                 |           3/2              3/2                         5/2               2          |                                                |/         2\                        3/2|                                                                        
                             /                       2                                                                  \                        |/        2\      /        2\        2        /        2\      /         2\           |                                                |\-1 + 25*x /*asin(5*x)   /        2\   |       /         2           \ /           2           \                
     /         2           \ |/         2           \          4                    2            /         2           \|                        \\1 - 25*x /      \1 - 25*x /   *asin (5*x)   \1 - 25*x /      \-1 + 25*x / *asin(5*x)/                                                \                         \1 - 25*x /   /   360*\-1 + tanh (2*(1 + x))/*\-1 + 2*tanh (2*(1 + x))/*tanh(2*(1 + x))
- 48*\-1 + tanh (2*(1 + x))/*\\-1 + tanh (2*(1 + x))/  + 2*tanh (2*(1 + x)) + 7*tanh (2*(1 + x))*\-1 + tanh (2*(1 + x))// - ------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------- - ---------------------------------------------------------------------
                                                                                                                                                                             asin(5*x)                                                                                           asin(5*x)                                                                    ___________                                
                                                                                                                                                                                                                                                                                                                                                             /         2                                 
                                                                                                                                                                                                                                                                                                                                                           \/  1 - 25*x  *asin(5*x)                      
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                asin(5*x)
450(5x(1−25x2)32+2(25x2−1)asin⁡(5x))(tanh⁡2(2(x+1))−1)tanh⁡2(2(x+1))asin⁡(5x)−48(tanh⁡2(2(x+1))−1)((tanh⁡2(2(x+1))−1)2+7(tanh⁡2(2(x+1))−1)tanh⁡2(2(x+1))+2tanh⁡4(2(x+1)))−125(75x2(1−25x2)52−30x(25x2−1)2asin⁡(5x)+1(1−25x2)32+6(1−25x2)32asin⁡2(5x))tanh⁡3(2(x+1))asin⁡(5x)−360(tanh⁡2(2(x+1))−1)(2tanh⁡2(2(x+1))−1)tanh⁡(2(x+1))1−25x2asin⁡(5x)asin⁡(5x)\frac{\frac{450 \left(\frac{5 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(25 x^{2} - 1\right) \operatorname{asin}{\left(5 x \right)}}\right) \left(\tanh^{2}{\left(2 \left(x + 1\right) \right)} - 1\right) \tanh^{2}{\left(2 \left(x + 1\right) \right)}}{\operatorname{asin}{\left(5 x \right)}} - 48 \left(\tanh^{2}{\left(2 \left(x + 1\right) \right)} - 1\right) \left(\left(\tanh^{2}{\left(2 \left(x + 1\right) \right)} - 1\right)^{2} + 7 \left(\tanh^{2}{\left(2 \left(x + 1\right) \right)} - 1\right) \tanh^{2}{\left(2 \left(x + 1\right) \right)} + 2 \tanh^{4}{\left(2 \left(x + 1\right) \right)}\right) - \frac{125 \left(\frac{75 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} - \frac{30 x}{\left(25 x^{2} - 1\right)^{2} \operatorname{asin}{\left(5 x \right)}} + \frac{1}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(5 x \right)}}\right) \tanh^{3}{\left(2 \left(x + 1\right) \right)}}{\operatorname{asin}{\left(5 x \right)}} - \frac{360 \left(\tanh^{2}{\left(2 \left(x + 1\right) \right)} - 1\right) \left(2 \tanh^{2}{\left(2 \left(x + 1\right) \right)} - 1\right) \tanh{\left(2 \left(x + 1\right) \right)}}{\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}}}{\operatorname{asin}{\left(5 x \right)}}
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Gráfico
Derivada de y=th^3(2x+2)/arcsin(5x)
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