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y=ln(x)/arcsin(x)
Derivada de la función/ ln(x)/ sin(x)/ arcsin/ y=ln(x)/arcsin(x)

Derivada de y=ln(x)/arcsin(x)

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

Ha introducido [src] 
 log(x)
-------
asin(x)
log⁡(x)asin⁡(x)\frac{\log{\left(x \right)}}{\operatorname{asin}{\left(x \right)}} 
log(x)/asin(x)
Gráfica
02468-8-6-4-2-1010-500500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    1              log(x)       
--------- - --------------------
x*asin(x)      ________         
              /      2      2   
            \/  1 - x  *asin (x)
−log⁡(x)1−x2asin⁡2(x)+1xasin⁡(x)- \frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}} + \frac{1}{x \operatorname{asin}{\left(x \right)}}
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Segunda derivada [src] 
 /     /     x                2        \                               \ 
 |     |----------- + -----------------|*log(x)                        | 
 |     |        3/2   /      2\        |                               | 
 |     |/     2\      \-1 + x /*asin(x)|                               | 
 |1    \\1 - x /                       /                    2          | 
-|-- + ---------------------------------------- + ---------------------| 
 | 2                   asin(x)                         ________        | 
 |x                                                   /      2         | 
 \                                                x*\/  1 - x  *asin(x)/ 
-------------------------------------------------------------------------
                                 asin(x)
−(x(1−x2)32+2(x2−1)asin⁡(x))log⁡(x)asin⁡(x)+2x1−x2asin⁡(x)+1x2asin⁡(x)- \frac{\frac{\left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right) \log{\left(x \right)}}{\operatorname{asin}{\left(x \right)}} + \frac{2}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{1}{x^{2}}}{\operatorname{asin}{\left(x \right)}}
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Tercera derivada [src] 
     /                     2                                               \                                                                      
     |     1            3*x                6                    6*x        |            /     x                2        \                         
     |----------- + ----------- + -------------------- - ------------------|*log(x)   3*|----------- + -----------------|                         
     |        3/2           5/2           3/2                     2        |            |        3/2   /      2\        |                         
     |/     2\      /     2\      /     2\        2      /      2\         |            |/     2\      \-1 + x /*asin(x)|                         
2    \\1 - x /      \1 - x /      \1 - x /   *asin (x)   \-1 + x / *asin(x)/            \\1 - x /                       /             3           
-- - ------------------------------------------------------------------------------ - ----------------------------------- + ----------------------
 3                                      asin(x)                                                    x*asin(x)                      ________        
x                                                                                                                            2   /      2         
                                                                                                                            x *\/  1 - x  *asin(x)
--------------------------------------------------------------------------------------------------------------------------------------------------
                                                                     asin(x)
−(3x2(1−x2)52−6x(x2−1)2asin⁡(x)+1(1−x2)32+6(1−x2)32asin⁡2(x))log⁡(x)asin⁡(x)−3(x(1−x2)32+2(x2−1)asin⁡(x))xasin⁡(x)+3x21−x2asin⁡(x)+2x3asin⁡(x)\frac{- \frac{\left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{6 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}}\right) \log{\left(x \right)}}{\operatorname{asin}{\left(x \right)}} - \frac{3 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right)}{x \operatorname{asin}{\left(x \right)}} + \frac{3}{x^{2} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{2}{x^{3}}}{\operatorname{asin}{\left(x \right)}}
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Gráfico
Derivada de y=ln(x)/arcsin(x)
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