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y=arcsinx^2/log^2x
Derivada de la función/ sinx^2/ arcsin/ y=arcsinx^2/log^2x

Derivada de y=arcsinx^2/log^2x

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

Ha introducido [src] 
    2   
asin (x)
--------
   2    
log (x)
asin⁡2(x)log⁡(x)2\frac{\operatorname{asin}^{2}{\left(x \right)}}{\log{\left(x \right)}^{2}} 
asin(x)^2/log(x)^2
Gráfica
02468-8-6-4-2-101005000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        2                         
  2*asin (x)        2*asin(x)     
- ---------- + -------------------
       3          ________        
  x*log (x)      /      2     2   
               \/  1 - x  *log (x)
2asin⁡(x)1−x2log⁡(x)2−2asin⁡2(x)xlog⁡(x)3\frac{2 \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \log{\left(x \right)}^{2}} - \frac{2 \operatorname{asin}^{2}{\left(x \right)}}{x \log{\left(x \right)}^{3}}
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Segunda derivada [src] 
  /                              2    /      3   \                       \
  |                          asin (x)*|1 + ------|                       |
  |     1       x*asin(x)             \    log(x)/        4*asin(x)      |
2*|- ------- + ----------- + --------------------- - --------------------|
  |        2           3/2          2                     ________       |
  |  -1 + x    /     2\            x *log(x)             /      2        |
  \            \1 - x /                              x*\/  1 - x  *log(x)/
--------------------------------------------------------------------------
                                    2                                     
                                 log (x)
2(xasin⁡(x)(1−x2)32−1x2−1−4asin⁡(x)x1−x2log⁡(x)+(1+3log⁡(x))asin⁡2(x)x2log⁡(x))log⁡(x)2\frac{2 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1} - \frac{4 \operatorname{asin}{\left(x \right)}}{x \sqrt{1 - x^{2}} \log{\left(x \right)}} + \frac{\left(1 + \frac{3}{\log{\left(x \right)}}\right) \operatorname{asin}^{2}{\left(x \right)}}{x^{2} \log{\left(x \right)}}\right)}{\log{\left(x \right)}^{2}}
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Tercera derivada [src] 
  /                             /     1       x*asin(x) \                                                                          \
  |                           6*|- ------- + -----------|                      2    /      9         12  \                         |
  |                             |        2           3/2|                  asin (x)*|2 + ------ + -------|     /      3   \        |
  |                             |  -1 + x    /     2\   |      2                    |    log(x)      2   |   6*|1 + ------|*asin(x)|
  |  asin(x)        3*x         \            \1 - x /   /   3*x *asin(x)            \             log (x)/     \    log(x)/        |
2*|----------- + ---------- - --------------------------- + ------------ - ------------------------------- + ----------------------|
  |        3/2            2             x*log(x)                    5/2                3                           ________        |
  |/     2\      /      2\                                  /     2\                  x *log(x)               2   /      2         |
  \\1 - x /      \-1 + x /                                  \1 - x /                                         x *\/  1 - x  *log(x) /
------------------------------------------------------------------------------------------------------------------------------------
                                                                 2                                                                  
                                                              log (x)
2(3x2asin⁡(x)(1−x2)52+3x(x2−1)2+asin⁡(x)(1−x2)32−6(xasin⁡(x)(1−x2)32−1x2−1)xlog⁡(x)+6(1+3log⁡(x))asin⁡(x)x21−x2log⁡(x)−(2+9log⁡(x)+12log⁡(x)2)asin⁡2(x)x3log⁡(x))log⁡(x)2\frac{2 \left(\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right)}{x \log{\left(x \right)}} + \frac{6 \left(1 + \frac{3}{\log{\left(x \right)}}\right) \operatorname{asin}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}} \log{\left(x \right)}} - \frac{\left(2 + \frac{9}{\log{\left(x \right)}} + \frac{12}{\log{\left(x \right)}^{2}}\right) \operatorname{asin}^{2}{\left(x \right)}}{x^{3} \log{\left(x \right)}}\right)}{\log{\left(x \right)}^{2}}
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Gráfico
Derivada de y=arcsinx^2/log^2x
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