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y=\sqrt(arcsin(1+2x^(3)))

Derivada de y=\sqrt(arcsin(1+2x^(3)))

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

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Solución

Ha introducido [src]
   ________________
  /     /       3\ 
\/  asin\1 + 2*x / 
$$\sqrt{\operatorname{asin}{\left(2 x^{3} + 1 \right)}}$$
sqrt(asin(1 + 2*x^3))
Gráfica
Primera derivada [src]
                      2                  
                   3*x                   
-----------------------------------------
    _________________                    
   /               2     ________________
  /      /       3\     /     /       3\ 
\/   1 - \1 + 2*x /  *\/  asin\1 + 2*x / 
$$\frac{3 x^{2}}{\sqrt{1 - \left(2 x^{3} + 1\right)^{2}} \sqrt{\operatorname{asin}{\left(2 x^{3} + 1 \right)}}}$$
Segunda derivada [src]
    /                                          3                      3 /       3\   \
    |          2                            3*x                    6*x *\1 + 2*x /   |
3*x*|--------------------- + --------------------------------- + --------------------|
    |    _________________   /               2\                                   3/2|
    |   /               2    |     /       3\ |     /       3\   /              2\   |
    |  /      /       3\     \-1 + \1 + 2*x / /*asin\1 + 2*x /   |    /       3\ |   |
    \\/   1 - \1 + 2*x /                                         \1 - \1 + 2*x / /   /
--------------------------------------------------------------------------------------
                                    ________________                                  
                                   /     /       3\                                   
                                 \/  asin\1 + 2*x /                                   
$$\frac{3 x \left(\frac{3 x^{3}}{\left(\left(2 x^{3} + 1\right)^{2} - 1\right) \operatorname{asin}{\left(2 x^{3} + 1 \right)}} + \frac{6 x^{3} \left(2 x^{3} + 1\right)}{\left(1 - \left(2 x^{3} + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{2}{\sqrt{1 - \left(2 x^{3} + 1\right)^{2}}}\right)}{\sqrt{\operatorname{asin}{\left(2 x^{3} + 1 \right)}}}$$
Tercera derivada [src]
  /                                                                                                                                                                   2                                      \
  |                                   6                             3                                    6                         3 /       3\           6 /       3\                  6 /       3\         |
  |          2                    36*x                          18*x                                 27*x                      36*x *\1 + 2*x /      108*x *\1 + 2*x /              54*x *\1 + 2*x /         |
3*|--------------------- + -------------------- + --------------------------------- + ------------------------------------ + -------------------- + -------------------- - ----------------------------------|
  |    _________________                    3/2   /               2\                                   3/2                                    3/2                    5/2                     2               |
  |   /               2    /              2\      |     /       3\ |     /       3\   /              2\                      /              2\      /              2\      /               2\                |
  |  /      /       3\     |    /       3\ |      \-1 + \1 + 2*x / /*asin\1 + 2*x /   |    /       3\ |        2/       3\   |    /       3\ |      |    /       3\ |      |     /       3\ |      /       3\|
  \\/   1 - \1 + 2*x /     \1 - \1 + 2*x / /                                          \1 - \1 + 2*x / /   *asin \1 + 2*x /   \1 - \1 + 2*x / /      \1 - \1 + 2*x / /      \-1 + \1 + 2*x / / *asin\1 + 2*x //
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                                                                                                ________________                                                                                              
                                                                                               /     /       3\                                                                                               
                                                                                             \/  asin\1 + 2*x /                                                                                               
$$\frac{3 \left(- \frac{54 x^{6} \left(2 x^{3} + 1\right)}{\left(\left(2 x^{3} + 1\right)^{2} - 1\right)^{2} \operatorname{asin}{\left(2 x^{3} + 1 \right)}} + \frac{36 x^{6}}{\left(1 - \left(2 x^{3} + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{27 x^{6}}{\left(1 - \left(2 x^{3} + 1\right)^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(2 x^{3} + 1 \right)}} + \frac{108 x^{6} \left(2 x^{3} + 1\right)^{2}}{\left(1 - \left(2 x^{3} + 1\right)^{2}\right)^{\frac{5}{2}}} + \frac{18 x^{3}}{\left(\left(2 x^{3} + 1\right)^{2} - 1\right) \operatorname{asin}{\left(2 x^{3} + 1 \right)}} + \frac{36 x^{3} \left(2 x^{3} + 1\right)}{\left(1 - \left(2 x^{3} + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{2}{\sqrt{1 - \left(2 x^{3} + 1\right)^{2}}}\right)}{\sqrt{\operatorname{asin}{\left(2 x^{3} + 1 \right)}}}$$
Gráfico
Derivada de y=\sqrt(arcsin(1+2x^(3)))