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asin((x-1)/x)
Derivada de la función/ (x-1)/ asin((x-1)/x)

Derivada de asin((x-1)/x)

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

Gráfico:

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Solución

Ha introducido [src] 
    /x - 1\
asin|-----|
    \  x  /
asin⁡(x−1x)\operatorname{asin}{\left(\frac{x - 1}{x} \right)} 
asin((x - 1)/x)
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
     1   x - 1      
     - - -----      
     x      2       
           x        
--------------------
      ______________
     /            2 
    /      (x - 1)  
   /   1 - -------- 
  /            2    
\/            x
1x−x−1x21−(x−1)2x2\frac{\frac{1}{x} - \frac{x - 1}{x^{2}}}{\sqrt{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}}}
Simplificar
Segunda derivada [src] 
             /     /    -1 + x\         \
             |     |1 - ------|*(-1 + x)|
/    -1 + x\ |     \      x   /         |
|1 - ------|*|-2 + ---------------------|
\      x   / |         /            2\  |
             |         |    (-1 + x) |  |
             |       x*|1 - ---------|  |
             |         |         2   |  |
             \         \        x    /  /
-----------------------------------------
                  _______________        
                 /             2         
          2     /      (-1 + x)          
         x *   /   1 - ---------         
              /             2            
            \/             x
(−2+(1−x−1x)(x−1)x(1−(x−1)2x2))(1−x−1x)x21−(x−1)2x2\frac{\left(-2 + \frac{\left(1 - \frac{x - 1}{x}\right) \left(x - 1\right)}{x \left(1 - \frac{\left(x - 1\right)^{2}}{x^{2}}\right)}\right) \left(1 - \frac{x - 1}{x}\right)}{x^{2} \sqrt{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}}}
Simplificar
Tercera derivada [src] 
             /                               2                                                      \
             |        4*(-1 + x)   3*(-1 + x)                                            2          |
             |    1 - ---------- + -----------     /    -1 + x\              /    -1 + x\          2|
             |            x              2       4*|1 - ------|*(-1 + x)   3*|1 - ------| *(-1 + x) |
/    -1 + x\ |                          x          \      x   /              \      x   /           |
|1 - ------|*|6 + ---------------------------- - ----------------------- + -------------------------|
\      x   / |                       2                /            2\                           2   |
             |               (-1 + x)                 |    (-1 + x) |            /            2\    |
             |           1 - ---------              x*|1 - ---------|          2 |    (-1 + x) |    |
             |                    2                   |         2   |         x *|1 - ---------|    |
             |                   x                    \        x    /            |         2   |    |
             \                                                                   \        x    /    /
-----------------------------------------------------------------------------------------------------
                                                _______________                                      
                                               /             2                                       
                                        3     /      (-1 + x)                                        
                                       x *   /   1 - ---------                                       
                                            /             2                                          
                                          \/             x
(1−x−1x)(6+1−4(x−1)x+3(x−1)2x21−(x−1)2x2−4(1−x−1x)(x−1)x(1−(x−1)2x2)+3(1−x−1x)2(x−1)2x2(1−(x−1)2x2)2)x31−(x−1)2x2\frac{\left(1 - \frac{x - 1}{x}\right) \left(6 + \frac{1 - \frac{4 \left(x - 1\right)}{x} + \frac{3 \left(x - 1\right)^{2}}{x^{2}}}{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}} - \frac{4 \left(1 - \frac{x - 1}{x}\right) \left(x - 1\right)}{x \left(1 - \frac{\left(x - 1\right)^{2}}{x^{2}}\right)} + \frac{3 \left(1 - \frac{x - 1}{x}\right)^{2} \left(x - 1\right)^{2}}{x^{2} \left(1 - \frac{\left(x - 1\right)^{2}}{x^{2}}\right)^{2}}\right)}{x^{3} \sqrt{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}}}
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Gráfico
Derivada de asin((x-1)/x)
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