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y=tg2x*arcsinx^3

Derivada de y=tg2x*arcsinx^3

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

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Solución

Ha introducido [src]
             3   
tan(2*x)*asin (x)
$$\tan{\left(2 x \right)} \operatorname{asin}^{3}{\left(x \right)}$$
tan(2*x)*asin(x)^3
Gráfica
Primera derivada [src]
                                   2            
    3    /         2     \   3*asin (x)*tan(2*x)
asin (x)*\2 + 2*tan (2*x)/ + -------------------
                                    ________    
                                   /      2     
                                 \/  1 - x      
$$\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \operatorname{asin}^{3}{\left(x \right)} + \frac{3 \tan{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
Segunda derivada [src]
/                                                                                /       2     \        \        
|  /     2       x*asin(x) \                  2    /       2     \            12*\1 + tan (2*x)/*asin(x)|        
|3*|- ------- + -----------|*tan(2*x) + 8*asin (x)*\1 + tan (2*x)/*tan(2*x) + --------------------------|*asin(x)
|  |        2           3/2|                                                            ________        |        
|  |  -1 + x    /     2\   |                                                           /      2         |        
\  \            \1 - x /   /                                                         \/  1 - x          /        
$$\left(3 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{x^{2} - 1}\right) \tan{\left(2 x \right)} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)} + \frac{12 \left(\tan^{2}{\left(2 x \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \operatorname{asin}{\left(x \right)}$$
Tercera derivada [src]
  /                    2          2     2                 \                                                                                                                          2    /       2     \         
  |     2          asin (x)    3*x *asin (x)   6*x*asin(x)|                   3    /       2     \ /         2     \      /       2     \ /     2       x*asin(x) \           72*asin (x)*\1 + tan (2*x)/*tan(2*x)
3*|----------- + ----------- + ------------- + -----------|*tan(2*x) + 16*asin (x)*\1 + tan (2*x)/*\1 + 3*tan (2*x)/ + 18*\1 + tan (2*x)/*|- ------- + -----------|*asin(x) + ------------------------------------
  |        3/2           3/2            5/2              2|                                                                               |        2           3/2|                          ________             
  |/     2\      /     2\       /     2\        /      2\ |                                                                               |  -1 + x    /     2\   |                         /      2              
  \\1 - x /      \1 - x /       \1 - x /        \-1 + x / /                                                                               \            \1 - x /   /                       \/  1 - x               
$$18 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{x^{2} - 1}\right) \left(\tan^{2}{\left(2 x \right)} + 1\right) \operatorname{asin}{\left(x \right)} + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(3 \tan^{2}{\left(2 x \right)} + 1\right) \operatorname{asin}^{3}{\left(x \right)} + 3 \left(\frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \tan{\left(2 x \right)} + \frac{72 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
Gráfico
Derivada de y=tg2x*arcsinx^3