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y=arcsinx^2/log2x
Derivada de la función/ log2x/ sinx^2/ arcsin/ y=arcsinx^2/log2x

Derivada de y=arcsinx^2/log2x

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

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Solución

Ha introducido [src] 
    2   
asin (x)
--------
log(2*x)
asin⁡2(x)log⁡(2x)\frac{\operatorname{asin}^{2}{\left(x \right)}}{\log{\left(2 x \right)}} 
asin(x)^2/log(2*x)
Gráfica
02468-8-6-4-2-1010-100005000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        2                           
    asin (x)         2*asin(x)      
- ----------- + --------------------
       2           ________         
  x*log (2*x)     /      2          
                \/  1 - x  *log(2*x)
2asin⁡(x)1−x2log⁡(2x)−asin⁡2(x)xlog⁡(2x)2\frac{2 \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \log{\left(2 x \right)}} - \frac{\operatorname{asin}^{2}{\left(x \right)}}{x \log{\left(2 x \right)}^{2}}
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Segunda derivada [src] 
                              2    /       2    \                         
                          asin (x)*|1 + --------|                         
     2      2*x*asin(x)            \    log(2*x)/         4*asin(x)       
- ------- + ----------- + ----------------------- - ----------------------
        2           3/2          2                       ________         
  -1 + x    /     2\            x *log(2*x)             /      2          
            \1 - x /                                x*\/  1 - x  *log(2*x)
--------------------------------------------------------------------------
                                 log(2*x)
2xasin⁡(x)(1−x2)32−2x2−1−4asin⁡(x)x1−x2log⁡(2x)+(1+2log⁡(2x))asin⁡2(x)x2log⁡(2x)log⁡(2x)\frac{\frac{2 x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{x^{2} - 1} - \frac{4 \operatorname{asin}{\left(x \right)}}{x \sqrt{1 - x^{2}} \log{\left(2 x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(2 x \right)}}\right) \operatorname{asin}^{2}{\left(x \right)}}{x^{2} \log{\left(2 x \right)}}}{\log{\left(2 x \right)}}
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Tercera derivada [src] 
  /                             /     1       x*asin(x) \                                                                                \
  |                           3*|- ------- + -----------|                      2    /       3           3    \                           |
  |                             |        2           3/2|                  asin (x)*|1 + -------- + ---------|     /       2    \        |
  |                             |  -1 + x    /     2\   |      2                    |    log(2*x)      2     |   3*|1 + --------|*asin(x)|
  |  asin(x)        3*x         \            \1 - x /   /   3*x *asin(x)            \               log (2*x)/     \    log(2*x)/        |
2*|----------- + ---------- - --------------------------- + ------------ - ----------------------------------- + ------------------------|
  |        3/2            2            x*log(2*x)                   5/2                 3                              ________          |
  |/     2\      /      2\                                  /     2\                   x *log(2*x)                2   /      2           |
  \\1 - x /      \-1 + x /                                  \1 - x /                                             x *\/  1 - x  *log(2*x) /
------------------------------------------------------------------------------------------------------------------------------------------
                                                                 log(2*x)
2(3x2asin⁡(x)(1−x2)52+3x(x2−1)2+asin⁡(x)(1−x2)32−3(xasin⁡(x)(1−x2)32−1x2−1)xlog⁡(2x)+3(1+2log⁡(2x))asin⁡(x)x21−x2log⁡(2x)−(1+3log⁡(2x)+3log⁡(2x)2)asin⁡2(x)x3log⁡(2x))log⁡(2x)\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{3 \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(2 x \right)}} + \frac{3 \left(1 + \frac{2}{\log{\left(2 x \right)}}\right) \operatorname{asin}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}} \log{\left(2 x \right)}} - \frac{\left(1 + \frac{3}{\log{\left(2 x \right)}} + \frac{3}{\log{\left(2 x \right)}^{2}}\right) \operatorname{asin}^{2}{\left(x \right)}}{x^{3} \log{\left(2 x \right)}}\right)}{\log{\left(2 x \right)}}
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Gráfico
Derivada de y=arcsinx^2/log2x
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