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atan(x/sqrt(1-x^2))-log(1+x*sqrt(1-x^2))
Derivada de la función/ atan(x/sqrt(1-x^2))-log(1+x*sqrt(1-x^2))

Derivada de atan(x/sqrt(1-x^2))-log(1+x*sqrt(1-x^2))

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

Gráfico:

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Solución

Ha introducido [src] 
                       /         ________\
    /     x     \      |        /      2 |
atan|-----------| - log\1 + x*\/  1 - x  /
    |   ________|                         
    |  /      2 |                         
    \\/  1 - x  /
−log⁡(x1−x2+1)+atan⁡(x1−x2)- \log{\left(x \sqrt{1 - x^{2}} + 1 \right)} + \operatorname{atan}{\left(\frac{x}{\sqrt{1 - x^{2}}} \right)} 
atan(x/sqrt(1 - x^2)) - log(1 + x*sqrt(1 - x^2))
Gráfica
02468-8-6-4-2-1010-510
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                    2          ________         2    
     1             x          /      2         x     
----------- + -----------   \/  1 - x   - -----------
   ________           3/2                    ________
  /      2    /     2\                      /      2 
\/  1 - x     \1 - x /                    \/  1 - x  
------------------------- - -------------------------
               2                         ________    
              x                         /      2     
        1 + ------              1 + x*\/  1 - x      
                 2                                   
            1 - x
x2(1−x2)32+11−x2x21−x2+1−−x21−x2+1−x2x1−x2+1\frac{\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{1 - x^{2}}}}{\frac{x^{2}}{1 - x^{2}} + 1} - \frac{- \frac{x^{2}}{\sqrt{1 - x^{2}}} + \sqrt{1 - x^{2}}}{x \sqrt{1 - x^{2}} + 1}
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Segunda derivada [src] 
                             2                                                                                                              
/     ________         2    \                                        /                           2  \                                       
|    /      2         x     |               /       2  \             |     1        2         3*x   |                 /       2  \          
|- \/  1 - x   + -----------|               |      x   |           x*|- ------- + ------ + ---------|                 |      x   |          
|                   ________|             x*|3 + ------|             |        2        2           2|             2*x*|1 + ------|          
|                  /      2 |               |         2|             |  -1 + x    1 - x    /     2\ |                 |         2|          
\                \/  1 - x  /               \    1 - x /             \                     \1 - x / /                 \    1 - x /          
------------------------------ + ------------------------------- - ---------------------------------- - ------------------------------------
                        2           ________ /         ________\          ________ /         2  \          ________           /         2  \
     /         ________\           /      2  |        /      2 |         /      2  |        x   |         /      2  /      2\ |        x   |
     |        /      2 |         \/  1 - x  *\1 + x*\/  1 - x  /       \/  1 - x  *|-1 + -------|       \/  1 - x  *\-1 + x /*|-1 + -------|
     \1 + x*\/  1 - x  /                                                           |           2|                             |           2|
                                                                                   \     -1 + x /                             \     -1 + x /
−x(3x2(1−x2)2−1x2−1+21−x2)1−x2(x2x2−1−1)+x(x21−x2+3)1−x2(x1−x2+1)−2x(x21−x2+1)1−x2(x2−1)(x2x2−1−1)+(x21−x2−1−x2)2(x1−x2+1)2- \frac{x \left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{2}} - \frac{1}{x^{2} - 1} + \frac{2}{1 - x^{2}}\right)}{\sqrt{1 - x^{2}} \left(\frac{x^{2}}{x^{2} - 1} - 1\right)} + \frac{x \left(\frac{x^{2}}{1 - x^{2}} + 3\right)}{\sqrt{1 - x^{2}} \left(x \sqrt{1 - x^{2}} + 1\right)} - \frac{2 x \left(\frac{x^{2}}{1 - x^{2}} + 1\right)}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)} + \frac{\left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)^{2}}{\left(x \sqrt{1 - x^{2}} + 1\right)^{2}}
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Tercera derivada [src] 
                               3                                                                                                                                                                                                                                            
  /     ________         2    \      /          4         2 \        /         4          2 \                                                  /                           2  \     /       2  \ /         2          4   \       /       2  \ /     ________         2    \
  |    /      2         x     |      |       5*x       6*x  |        |        x        2*x  |                    /       2  \                2 |     1        2         3*x   |     |      x   | |      5*x        4*x    |       |      x   | |    /      2         x     |
2*|- \/  1 - x   + -----------|    3*|1 + --------- + ------|      3*|1 + --------- + ------|                  2 |      x   |             4*x *|- ------- + ------ + ---------|   2*|1 + ------|*|1 - ------- + ----------|   3*x*|3 + ------|*|- \/  1 - x   + -----------|
  |                   ________|      |            2        2|        |            2        2|               8*x *|1 + ------|                  |        2        2           2|     |         2| |          2            2|       |         2| |                   ________|
  |                  /      2 |      |    /     2\    1 - x |        |    /     2\    1 - x |                    |         2|                  |  -1 + x    1 - x    /     2\ |     \    1 - x / |    -1 + x    /      2\ |       \    1 - x / |                  /      2 |
  \                \/  1 - x  /      \    \1 - x /          /        \    \1 - x /          /                    \    1 - x /                  \                     \1 - x / /                  \              \-1 + x / /                    \                \/  1 - x  /
-------------------------------- - -------------------------- + ------------------------------- - ------------------------------------- - ------------------------------------- + ----------------------------------------- + ----------------------------------------------
                         3                 3/2 /         2  \      ________ /         ________\      ________          2 /         2  \       ________           /         2  \                                         2                                           2       
      /         ________\          /     2\    |        x   |     /      2  |        /      2 |     /      2  /      2\  |        x   |      /      2  /      2\ |        x   |        ________           /         2  \                ________ /         ________\        
      |        /      2 |          \1 - x /   *|-1 + -------|   \/  1 - x  *\1 + x*\/  1 - x  /   \/  1 - x  *\-1 + x / *|-1 + -------|    \/  1 - x  *\-1 + x /*|-1 + -------|       /      2  /      2\ |        x   |               /      2  |        /      2 |        
      \1 + x*\/  1 - x  /                      |           2|                                                            |           2|                          |           2|     \/  1 - x  *\-1 + x /*|-1 + -------|             \/  1 - x  *\1 + x*\/  1 - x  /        
                                               \     -1 + x /                                                            \     -1 + x /                          \     -1 + x /                           |           2|                                                    
                                                                                                                                                                                                          \     -1 + x /
−4x2(3x2(1−x2)2−1x2−1+21−x2)1−x2(x2−1)(x2x2−1−1)−8x2(x21−x2+1)1−x2(x2−1)2(x2x2−1−1)+3x(x21−x2+3)(x21−x2−1−x2)1−x2(x1−x2+1)2+2(x21−x2−1−x2)3(x1−x2+1)3+3(x4(1−x2)2+2x21−x2+1)1−x2(x1−x2+1)+2(x21−x2+1)(4x4(x2−1)2−5x2x2−1+1)1−x2(x2−1)(x2x2−1−1)2−3(5x4(1−x2)2+6x21−x2+1)(1−x2)32(x2x2−1−1)- \frac{4 x^{2} \left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{2}} - \frac{1}{x^{2} - 1} + \frac{2}{1 - x^{2}}\right)}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)} - \frac{8 x^{2} \left(\frac{x^{2}}{1 - x^{2}} + 1\right)}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right)^{2} \left(\frac{x^{2}}{x^{2} - 1} - 1\right)} + \frac{3 x \left(\frac{x^{2}}{1 - x^{2}} + 3\right) \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)}{\sqrt{1 - x^{2}} \left(x \sqrt{1 - x^{2}} + 1\right)^{2}} + \frac{2 \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)^{3}}{\left(x \sqrt{1 - x^{2}} + 1\right)^{3}} + \frac{3 \left(\frac{x^{4}}{\left(1 - x^{2}\right)^{2}} + \frac{2 x^{2}}{1 - x^{2}} + 1\right)}{\sqrt{1 - x^{2}} \left(x \sqrt{1 - x^{2}} + 1\right)} + \frac{2 \left(\frac{x^{2}}{1 - x^{2}} + 1\right) \left(\frac{4 x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{5 x^{2}}{x^{2} - 1} + 1\right)}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)^{2}} - \frac{3 \left(\frac{5 x^{4}}{\left(1 - x^{2}\right)^{2}} + \frac{6 x^{2}}{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\frac{x^{2}}{x^{2} - 1} - 1\right)}
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Gráfico
Derivada de atan(x/sqrt(1-x^2))-log(1+x*sqrt(1-x^2))
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