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y=x*arcsin(1/x)+ln(x*sqrt(x^2-1))
Derivada de la función/ y=x*arcsin(1/x)+ln(x*sqrt(x^2-1))

Derivada de y=x*arcsin(1/x)+ln(x*sqrt(x^2-1))

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

Gráfico:

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Solución

Ha introducido [src] 
               /     ________\
      /1\      |    /  2     |
x*asin|-| + log\x*\/  x  - 1 /
      \x/
xasin⁡(1x)+log⁡(xx2−1)x \operatorname{asin}{\left(\frac{1}{x} \right)} + \log{\left(x \sqrt{x^{2} - 1} \right)} 
x*asin(1/x) + log(x*sqrt(x^2 - 1))
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                       ________         2              
                      /  2             x               
                    \/  x  - 1  + -----------          
                                     ________          
                                    /  2               
         1                        \/  x  - 1        /1\
- --------------- + ------------------------- + asin|-|
         ________              ________             \x/
        /     1               /  2                     
  x*   /  1 - --          x*\/  x  - 1                 
      /        2                                       
    \/        x
asin⁡(1x)+x2x2−1+x2−1xx2−1−1x1−1x2\operatorname{asin}{\left(\frac{1}{x} \right)} + \frac{\frac{x^{2}}{\sqrt{x^{2} - 1}} + \sqrt{x^{2} - 1}}{x \sqrt{x^{2} - 1}} - \frac{1}{x \sqrt{1 - \frac{1}{x^{2}}}}
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Segunda derivada [src] 
                                   _________         2           _________         2     
                          2       /       2         x           /       2         x      
                         x      \/  -1 + x   + ------------   \/  -1 + x   + ------------
                 -3 + -------                     _________                     _________
                            2                    /       2                     /       2 
      1               -1 + x                   \/  -1 + x                    \/  -1 + x  
-------------- - ------------ - --------------------------- - ---------------------------
           3/2           2                       3/2                      _________      
 4 /    1 \        -1 + x               /      2\                    2   /       2       
x *|1 - --|                             \-1 + x /                   x *\/  -1 + x        
   |     2|                                                                              
   \    x /
−x2x2−1−3x2−1−x2x2−1+x2−1(x2−1)32−x2x2−1+x2−1x2x2−1+1x4(1−1x2)32- \frac{\frac{x^{2}}{x^{2} - 1} - 3}{x^{2} - 1} - \frac{\frac{x^{2}}{\sqrt{x^{2} - 1}} + \sqrt{x^{2} - 1}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} - \frac{\frac{x^{2}}{\sqrt{x^{2} - 1}} + \sqrt{x^{2} - 1}}{x^{2} \sqrt{x^{2} - 1}} + \frac{1}{x^{4} \left(1 - \frac{1}{x^{2}}\right)^{\frac{3}{2}}}
Simplificar
Tercera derivada [src] 
                                       _________         2                                                  /   _________         2     \       /   _________         2     \     /         4            2 \
                                      /       2         x             /         2  \     /         2  \     |  /       2         x      |       |  /       2         x      |     |        x          2*x  |
                                    \/  -1 + x   + ------------       |        x   |     |        x   |   2*|\/  -1 + x   + ------------|   3*x*|\/  -1 + x   + ------------|   3*|1 + ---------- - -------|
                                                      _________   2*x*|-3 + -------|   2*|-3 + -------|     |                  _________|       |                  _________|     |             2         2|
                                                     /       2        |           2|     |           2|     |                 /       2 |       |                 /       2 |     |    /      2\    -1 + x |
        4                3                         \/  -1 + x         \     -1 + x /     \     -1 + x /     \               \/  -1 + x  /       \               \/  -1 + x  /     \    \-1 + x /           /
- -------------- - -------------- + --------------------------- + ------------------ + ---------------- + ------------------------------- + --------------------------------- + ----------------------------
             3/2              5/2                     3/2                      2           /      2\                    _________                               5/2                       /      2\         
   5 /    1 \       7 /    1 \               /      2\                /      2\          x*\-1 + x /               3   /       2                       /      2\                        x*\-1 + x /         
  x *|1 - --|      x *|1 - --|             x*\-1 + x /                \-1 + x /                                   x *\/  -1 + x                        \-1 + x /                                            
     |     2|         |     2|                                                                                                                                                                              
     \    x /         \    x /
2x(x2x2−1−3)(x2−1)2+3x(x2x2−1+x2−1)(x2−1)52+2(x2x2−1−3)x(x2−1)+3(x4(x2−1)2−2x2x2−1+1)x(x2−1)+x2x2−1+x2−1x(x2−1)32+2(x2x2−1+x2−1)x3x2−1−4x5(1−1x2)32−3x7(1−1x2)52\frac{2 x \left(\frac{x^{2}}{x^{2} - 1} - 3\right)}{\left(x^{2} - 1\right)^{2}} + \frac{3 x \left(\frac{x^{2}}{\sqrt{x^{2} - 1}} + \sqrt{x^{2} - 1}\right)}{\left(x^{2} - 1\right)^{\frac{5}{2}}} + \frac{2 \left(\frac{x^{2}}{x^{2} - 1} - 3\right)}{x \left(x^{2} - 1\right)} + \frac{3 \left(\frac{x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{2 x^{2}}{x^{2} - 1} + 1\right)}{x \left(x^{2} - 1\right)} + \frac{\frac{x^{2}}{\sqrt{x^{2} - 1}} + \sqrt{x^{2} - 1}}{x \left(x^{2} - 1\right)^{\frac{3}{2}}} + \frac{2 \left(\frac{x^{2}}{\sqrt{x^{2} - 1}} + \sqrt{x^{2} - 1}\right)}{x^{3} \sqrt{x^{2} - 1}} - \frac{4}{x^{5} \left(1 - \frac{1}{x^{2}}\right)^{\frac{3}{2}}} - \frac{3}{x^{7} \left(1 - \frac{1}{x^{2}}\right)^{\frac{5}{2}}}
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Gráfico
Derivada de y=x*arcsin(1/x)+ln(x*sqrt(x^2-1))
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