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(arccosx)/(arcsinx^2)
Derivada de la función/ arccos/ sinx^2/ arcsin/ (arccosx)/(arcsinx^2)

Derivada de (arccosx)/(arcsinx^2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
acos(x) 
--------
    2   
asin (x)
acos⁡(x)asin⁡2(x)\frac{\operatorname{acos}{\left(x \right)}}{\operatorname{asin}^{2}{\left(x \right)}} 
acos(x)/asin(x)^2
Gráfica
02468-8-6-4-2-1010-50005000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
           1                  2*acos(x)      
- -------------------- - --------------------
     ________               ________         
    /      2      2        /      2      3   
  \/  1 - x  *asin (x)   \/  1 - x  *asin (x)
−2acos⁡(x)1−x2asin⁡3(x)−11−x2asin⁡2(x)- \frac{2 \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{3}{\left(x \right)}} - \frac{1}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}
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Segunda derivada [src] 
 /                                    /     x                3        \        \ 
 |                                  2*|----------- + -----------------|*acos(x)| 
 |                                    |        3/2   /      2\        |        | 
 |                                    |/     2\      \-1 + x /*asin(x)|        | 
 |     x                4             \\1 - x /                       /        | 
-|----------- + ----------------- + -------------------------------------------| 
 |        3/2   /      2\                             asin(x)                  | 
 |/     2\      \-1 + x /*asin(x)                                              | 
 \\1 - x /                                                                     / 
---------------------------------------------------------------------------------
                                         2                                       
                                     asin (x)
−x(1−x2)32+2(x(1−x2)32+3(x2−1)asin⁡(x))acos⁡(x)asin⁡(x)+4(x2−1)asin⁡(x)asin⁡2(x)- \frac{\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right) \operatorname{acos}{\left(x \right)}}{\operatorname{asin}{\left(x \right)}} + \frac{4}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}}{\operatorname{asin}^{2}{\left(x \right)}}
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Tercera derivada [src] 
                 /                     2                                               \                                                                   
          2      |     1            3*x                12                   9*x        |                                  /     x                3        \
       3*x     2*|----------- + ----------- + -------------------- - ------------------|*acos(x)                        6*|----------- + -----------------|
-1 + -------     |        3/2           5/2           3/2                     2        |                                  |        3/2   /      2\        |
           2     |/     2\      /     2\      /     2\        2      /      2\         |                                  |/     2\      \-1 + x /*asin(x)|
     -1 + x      \\1 - x /      \1 - x /      \1 - x /   *asin (x)   \-1 + x / *asin(x)/                  6*x             \\1 - x /                       /
------------ - --------------------------------------------------------------------------------- + ------------------ + -----------------------------------
        3/2                                         asin(x)                                                 2                      ________                
/     2\                                                                                           /      2\                      /      2                 
\1 - x /                                                                                           \-1 + x / *asin(x)           \/  1 - x  *asin(x)        
-----------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                              2                                                                            
                                                                          asin (x)
6x(x2−1)2asin⁡(x)−2(3x2(1−x2)52−9x(x2−1)2asin⁡(x)+1(1−x2)32+12(1−x2)32asin⁡2(x))acos⁡(x)asin⁡(x)+6(x(1−x2)32+3(x2−1)asin⁡(x))1−x2asin⁡(x)+3x2x2−1−1(1−x2)32asin⁡2(x)\frac{\frac{6 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} - \frac{2 \left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{9 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{12}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}}\right) \operatorname{acos}{\left(x \right)}}{\operatorname{asin}{\left(x \right)}} + \frac{6 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right)}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{\operatorname{asin}^{2}{\left(x \right)}}
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Gráfico
Derivada de (arccosx)/(arcsinx^2)
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