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y=th3(2x+2)/arcsin(5x)

Derivada de y=th3(2x+2)/arcsin(5x)

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Solución

Ha introducido [src]
tanh(3)*(2*x + 2)
-----------------
    asin(5*x)    
$$\frac{\left(2 x + 2\right) \tanh{\left(3 \right)}}{\operatorname{asin}{\left(5 x \right)}}$$
(tanh(3)*(2*x + 2))/asin(5*x)
Gráfica
Primera derivada [src]
2*tanh(3)      5*(2*x + 2)*tanh(3)   
--------- - -------------------------
asin(5*x)      ___________           
              /         2      2     
            \/  1 - 25*x  *asin (5*x)
$$\frac{2 \tanh{\left(3 \right)}}{\operatorname{asin}{\left(5 x \right)}} - \frac{5 \left(2 x + 2\right) \tanh{\left(3 \right)}}{\sqrt{1 - 25 x^{2}} \operatorname{asin}^{2}{\left(5 x \right)}}$$
Segunda derivada [src]
    /      2                    /          2                   5*x      \\        
-10*|-------------- + 5*(1 + x)*|---------------------- + --------------||*tanh(3)
    |   ___________             |/         2\                        3/2||        
    |  /         2              |\-1 + 25*x /*asin(5*x)   /        2\   ||        
    \\/  1 - 25*x               \                         \1 - 25*x /   //        
----------------------------------------------------------------------------------
                                        2                                         
                                    asin (5*x)                                    
$$- \frac{10 \left(5 \left(x + 1\right) \left(\frac{5 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(25 x^{2} - 1\right) \operatorname{asin}{\left(5 x \right)}}\right) + \frac{2}{\sqrt{1 - 25 x^{2}}}\right) \tanh{\left(3 \right)}}{\operatorname{asin}^{2}{\left(5 x \right)}}$$
Tercera derivada [src]
    /          /                                                     2                               \                                          \        
    |          |      1                      6                   75*x                   30*x         |             6                   15*x     |        
-50*|5*(1 + x)*|-------------- + ------------------------- + -------------- - -----------------------| + ---------------------- + --------------|*tanh(3)
    |          |           3/2              3/2                         5/2               2          |   /         2\                        3/2|        
    |          |/        2\      /        2\        2        /        2\      /         2\           |   \-1 + 25*x /*asin(5*x)   /        2\   |        
    \          \\1 - 25*x /      \1 - 25*x /   *asin (5*x)   \1 - 25*x /      \-1 + 25*x / *asin(5*x)/                            \1 - 25*x /   /        
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                                                                            2                                                                            
                                                                        asin (5*x)                                                                       
$$- \frac{50 \left(\frac{15 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + 5 \left(x + 1\right) \left(\frac{75 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} - \frac{30 x}{\left(25 x^{2} - 1\right)^{2} \operatorname{asin}{\left(5 x \right)}} + \frac{1}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(5 x \right)}}\right) + \frac{6}{\left(25 x^{2} - 1\right) \operatorname{asin}{\left(5 x \right)}}\right) \tanh{\left(3 \right)}}{\operatorname{asin}^{2}{\left(5 x \right)}}$$
Gráfico
Derivada de y=th3(2x+2)/arcsin(5x)