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

Derivada de y=x*arctan(sqrt(x^2-1))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
      /          2\
      |  / 2    \ |
x*atan\t*\x  - 1/ /
xatan⁡(t(x2−1)2)x \operatorname{atan}{\left(t \left(x^{2} - 1\right)^{2} \right)} 
x*atan(t*(x^2 - 1)^2)
Primera derivada [src] 
     2 / 2    \        /          2\
4*t*x *\x  - 1/        |  / 2    \ |
---------------- + atan\t*\x  - 1/ /
               4                    
     2 / 2    \                     
1 + t *\x  - 1/
4tx2(x2−1)t2(x2−1)4+1+atan⁡(t(x2−1)2)\frac{4 t x^{2} \left(x^{2} - 1\right)}{t^{2} \left(x^{2} - 1\right)^{4} + 1} + \operatorname{atan}{\left(t \left(x^{2} - 1\right)^{2} \right)}
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Segunda derivada [src] 
      /                             4\
      |               2  2 /      2\ |
      |        2   8*t *x *\-1 + x / |
4*t*x*|-3 + 5*x  - ------------------|
      |                            4 |
      |                 2 /      2\  |
      \            1 + t *\-1 + x /  /
--------------------------------------
                          4           
               2 /      2\            
          1 + t *\-1 + x /
4tx(−8t2x2(x2−1)4t2(x2−1)4+1+5x2−3)t2(x2−1)4+1\frac{4 t x \left(- \frac{8 t^{2} x^{2} \left(x^{2} - 1\right)^{4}}{t^{2} \left(x^{2} - 1\right)^{4} + 1} + 5 x^{2} - 3\right)}{t^{2} \left(x^{2} - 1\right)^{4} + 1}
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Tercera derivada [src] 
    /                 /                    4                     3                     7 \                     4\
    |                 |         2 /      2\        2  2 /      2\        4  2 /      2\  |       2  2 /      2\ |
    |        2      2 |     12*t *\-1 + x /    40*t *x *\-1 + x /    64*t *x *\-1 + x /  |   24*t *x *\-1 + x / |
4*t*|-3 + 9*x  + 2*x *|3 - ----------------- - ------------------- + --------------------| - -------------------|
    |                 |                    4                    4                       2|                    4 |
    |                 |         2 /      2\          2 /      2\     /                4\ |         2 /      2\  |
    |                 |    1 + t *\-1 + x /     1 + t *\-1 + x /     |     2 /      2\ | |    1 + t *\-1 + x /  |
    \                 \                                              \1 + t *\-1 + x / / /                      /
-----------------------------------------------------------------------------------------------------------------
                                                                4                                                
                                                     2 /      2\                                                 
                                                1 + t *\-1 + x /
4t(−24t2x2(x2−1)4t2(x2−1)4+1+2x2(64t4x2(x2−1)7(t2(x2−1)4+1)2−40t2x2(x2−1)3t2(x2−1)4+1−12t2(x2−1)4t2(x2−1)4+1+3)+9x2−3)t2(x2−1)4+1\frac{4 t \left(- \frac{24 t^{2} x^{2} \left(x^{2} - 1\right)^{4}}{t^{2} \left(x^{2} - 1\right)^{4} + 1} + 2 x^{2} \left(\frac{64 t^{4} x^{2} \left(x^{2} - 1\right)^{7}}{\left(t^{2} \left(x^{2} - 1\right)^{4} + 1\right)^{2}} - \frac{40 t^{2} x^{2} \left(x^{2} - 1\right)^{3}}{t^{2} \left(x^{2} - 1\right)^{4} + 1} - \frac{12 t^{2} \left(x^{2} - 1\right)^{4}}{t^{2} \left(x^{2} - 1\right)^{4} + 1} + 3\right) + 9 x^{2} - 3\right)}{t^{2} \left(x^{2} - 1\right)^{4} + 1}
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3-я производная [src] 
    /                 /                    4                     3                     7 \                     4\
    |                 |         2 /      2\        2  2 /      2\        4  2 /      2\  |       2  2 /      2\ |
    |        2      2 |     12*t *\-1 + x /    40*t *x *\-1 + x /    64*t *x *\-1 + x /  |   24*t *x *\-1 + x / |
4*t*|-3 + 9*x  + 2*x *|3 - ----------------- - ------------------- + --------------------| - -------------------|
    |                 |                    4                    4                       2|                    4 |
    |                 |         2 /      2\          2 /      2\     /                4\ |         2 /      2\  |
    |                 |    1 + t *\-1 + x /     1 + t *\-1 + x /     |     2 /      2\ | |    1 + t *\-1 + x /  |
    \                 \                                              \1 + t *\-1 + x / / /                      /
-----------------------------------------------------------------------------------------------------------------
                                                                4                                                
                                                     2 /      2\                                                 
                                                1 + t *\-1 + x /
4t(−24t2x2(x2−1)4t2(x2−1)4+1+2x2(64t4x2(x2−1)7(t2(x2−1)4+1)2−40t2x2(x2−1)3t2(x2−1)4+1−12t2(x2−1)4t2(x2−1)4+1+3)+9x2−3)t2(x2−1)4+1\frac{4 t \left(- \frac{24 t^{2} x^{2} \left(x^{2} - 1\right)^{4}}{t^{2} \left(x^{2} - 1\right)^{4} + 1} + 2 x^{2} \left(\frac{64 t^{4} x^{2} \left(x^{2} - 1\right)^{7}}{\left(t^{2} \left(x^{2} - 1\right)^{4} + 1\right)^{2}} - \frac{40 t^{2} x^{2} \left(x^{2} - 1\right)^{3}}{t^{2} \left(x^{2} - 1\right)^{4} + 1} - \frac{12 t^{2} \left(x^{2} - 1\right)^{4}}{t^{2} \left(x^{2} - 1\right)^{4} + 1} + 3\right) + 9 x^{2} - 3\right)}{t^{2} \left(x^{2} - 1\right)^{4} + 1}
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