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Derivada de la función/ x^2-a^2/ y=ln|x+sqr(x^2-a^2)|

Derivada de y=ln|x+sqr(x^2-a^2)|

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   /|             2|\
   ||    / 2    2\ ||
log\|x + \x  - a / |/
log⁡(∣x+(−a2+x2)2∣)\log{\left(\left|{x + \left(- a^{2} + x^{2}\right)^{2}}\right| \right)} 
log(Abs(x + (x^2 - a^2)^2))
Primera derivada [src] 
/                                 /                          2                  \                                            \     /             2\
|/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \|     |    / 2    2\ |
\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)//*sign\x + \x  - a / /
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                                                         \x + \x  - a / /*|x + \x  - a / |
(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))sign⁡(x+(−a2+x2)2)(x+(−a2+x2)2)∣x+(−a2+x2)2∣\frac{\left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \operatorname{sign}{\left(x + \left(- a^{2} + x^{2}\right)^{2} \right)}}{\left(x + \left(- a^{2} + x^{2}\right)^{2}\right) \left|{x + \left(- a^{2} + x^{2}\right)^{2}}\right|}
Simplificar
Segunda derivada [src] 
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/                                 /                          2                  \                                            \   /    /             2\\   /                                2     /                          2                  \                                                                                         \     /             2\   /         / 2    2\\ |/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \|     |    / 2    2\ |   |/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \|      2|    / 2    2\ |
|/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \| d |    |    / 2    2\ ||   |/        / 2     2        2   \\      |    / 2     2        2   \        2      2   | /  2        2         2\        2      2    / 2     2        2   \       2   2      2   |     |    / 2    2\ |   \-1 + 4*x*\a  - x //*\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)//*sign\x + \a  - x / /   \\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)// *sign \x + \a  - x / /
\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)//*--\sign\x + \a  - x / // + \\1 + 4*x*\x  + im (a) - re (a)//  + 4*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/*\im (a) - re (a) + 3*x / + 32*im (a)*re (a)*\x  + im (a) - re (a)/ + 64*x *im (a)*re (a)/*sign\x + \a  - x / / + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                               dx                                                                                                                                                                                                                                                                                                                           2                                                                                                                                          /             2\ |             2|                                                          
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                                                                                                                                                                                                                                                                                                                                                                                                                                               x + \a  - x /                                                                                                                                           \x + \a  - x / /*|x + \a  - x / |                                                          
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                                                                                                                                                                                                                                                                                                                                \x + \a  - x / /*|x + \a  - x / |
(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))∂∂xsign⁡(x+(a2−x2)2)+(64x2(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)2+4(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2)(3x2−(re⁡(a))2+(im⁡(a))2)+32(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2)sign⁡(x+(a2−x2)2)+(4x(a2−x2)−1)(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))sign⁡(x+(a2−x2)2)x+(a2−x2)2−(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))2sign⁡2(x+(a2−x2)2)(x+(a2−x2)2)∣x+(a2−x2)2∣(x+(a2−x2)2)∣x+(a2−x2)2∣\frac{\left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + \left(64 x^{2} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right)^{2} + 4 \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 32 \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + \frac{\left(4 x \left(a^{2} - x^{2}\right) - 1\right) \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{x + \left(a^{2} - x^{2}\right)^{2}} - \frac{\left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right)^{2} \operatorname{sign}^{2}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|}
Simplificar
Tercera derivada [src] 
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                2 /                                 /                          2                  \                                            \     /             2\     /         / 2    2\\ |/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \| d |    |    / 2    2\ ||                          /                                2     /                          2                  \                                                                                         \     /             2\     /                                 /                          2                  \                                            \       /             2\                 /                                 /                          2                  \                                            \     /             2\     |/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \|  d |    |    / 2    2\ ||     |    / 2    2\ |          /             2\ /                                 /                          2                  \                                            \ /                                2     /                          2                  \                                                                                         \     /                                 /                          2                  \                                            \       /             2\                     
/                                 /                          2                  \                                            \   2/    /             2\\     /                                2     /                          2                  \                                                                                         \   /    /             2\\      /                                                                /                          2                  \                     \     /             2\     /         / 2    2\\  |/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \|     |    / 2    2\ |   2*\-1 + 4*x*\a  - x //*\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)//*--\sign\x + \a  - x / //     /         / 2    2\\ |/        / 2     2        2   \\      |    / 2     2        2   \        2      2   | /  2        2         2\        2      2    / 2     2        2   \       2   2      2   |     |    / 2    2\ |     |/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \|      3|    / 2    2\ |     / 2      2\ |/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \|     |    / 2    2\ |   3*\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)// *--\sign\x + \a  - x / //*sign\x + \a  - x / /         2|    / 2    2\ | |/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \| |/        / 2     2        2   \\      |    / 2     2        2   \        2      2   | /  2        2         2\        2      2    / 2     2        2   \       2   2      2   |     |/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \|      2|    / 2    2\ | /         / 2    2\\
|/        / 2     2        2   \\ |    / 2     2        2   \        2      2   |          2      2    / 2     2        2   \|  d |    |    / 2    2\ ||     |/        / 2     2        2   \\      |    / 2     2        2   \        2      2   | /  2        2         2\        2      2    / 2     2        2   \       2   2      2   | d |    |    / 2    2\ ||      |/        / 2     2        2   \\ /  2        2         2\       |    / 2     2        2   \        2      2   |          2      2   |     |    / 2    2\ |   2*\-1 + 4*x*\a  - x // *\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)//*sign\x + \a  - x / /                                                                                                                                                         dx                         2*\-1 + 4*x*\a  - x //*\\1 + 4*x*\x  + im (a) - re (a)//  + 4*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/*\im (a) - re (a) + 3*x / + 32*im (a)*re (a)*\x  + im (a) - re (a)/ + 64*x *im (a)*re (a)/*sign\x + \a  - x / /   2*\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)// *sign \x + \a  - x / /   4*\a  - 3*x /*\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)//*sign\x + \a  - x / /                                                                                                                                     dx                                              3*sign \x + \a  - x / /*\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)//*\\1 + 4*x*\x  + im (a) - re (a)//  + 4*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/*\im (a) - re (a) + 3*x / + 32*im (a)*re (a)*\x  + im (a) - re (a)/ + 64*x *im (a)*re (a)/   3*\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)// *sign \x + \a  - x / /*\-1 + 4*x*\a  - x //
\\1 + 4*x*\x  + im (a) - re (a)//*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x  + im (a) - re (a)//*---\sign\x + \a  - x / // + 2*\\1 + 4*x*\x  + im (a) - re (a)//  + 4*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/*\im (a) - re (a) + 3*x / + 32*im (a)*re (a)*\x  + im (a) - re (a)/ + 64*x *im (a)*re (a)/*--\sign\x + \a  - x / // + 12*\\1 + 4*x*\x  + im (a) - re (a)//*\im (a) - re (a) + 3*x / + 2*x*\x + \x  + im (a) - re (a)/  - 4*im (a)*re (a)/ + 16*x*im (a)*re (a)/*sign\x + \a  - x / / + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                 2                                                                                                                                                                                                            dx                                                                                                                                                                                                                                                                                       2                                                                                                                                                                             2                                                                                                                                                                                                       2                                                                                                                                                                                    2                 2                                                                                                                                                    2                                                                                                                                                   /             2\ |             2|                                                                                                                                                                                                                             /             2\ |             2|                                                                                                                                                                                                                                           2                                                                                      
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |    / 2    2\ |                                                                                                                                                                 x + \a  - x /                                                                                                                                                                                           x + \a  - x /                                                                                                                                                                     |    / 2    2\ |  |    / 2    2\ |                                                                                                                                        x + \a  - x /                                                                                                                                                    \x + \a  - x / /*|x + \a  - x / |                                                                                                                                                                                                                             \x + \a  - x / /*|x + \a  - x / |                                                                                                                                                                                                                           |    / 2    2\ |  |    / 2    2\ |                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \x + \a  - x / /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \x + \a  - x / / *|x + \a  - x / |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \x + \a  - x / / *|x + \a  - x / |                                                                     
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \x + \a  - x / /*|x + \a  - x / |
4(a2−3x2)(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))sign⁡(x+(a2−x2)2)x+(a2−x2)2+(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))∂2∂x2sign⁡(x+(a2−x2)2)+12(2x(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2)+16x(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(3x2−(re⁡(a))2+(im⁡(a))2))sign⁡(x+(a2−x2)2)+2(64x2(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)2+4(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2)(3x2−(re⁡(a))2+(im⁡(a))2)+32(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2)∂∂xsign⁡(x+(a2−x2)2)+2(4x(a2−x2)−1)(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))∂∂xsign⁡(x+(a2−x2)2)x+(a2−x2)2+2(4x(a2−x2)−1)(64x2(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)2+4(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2)(3x2−(re⁡(a))2+(im⁡(a))2)+32(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2)sign⁡(x+(a2−x2)2)x+(a2−x2)2−3(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))2sign⁡(x+(a2−x2)2)∂∂xsign⁡(x+(a2−x2)2)(x+(a2−x2)2)∣x+(a2−x2)2∣−3(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))(64x2(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)2+4(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2)(3x2−(re⁡(a))2+(im⁡(a))2)+32(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2)sign⁡2(x+(a2−x2)2)(x+(a2−x2)2)∣x+(a2−x2)2∣+2(4x(a2−x2)−1)2(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))sign⁡(x+(a2−x2)2)(x+(a2−x2)2)2−3(4x(a2−x2)−1)(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))2sign⁡2(x+(a2−x2)2)(x+(a2−x2)2)2∣x+(a2−x2)2∣+2(32x(x2−(re⁡(a))2+(im⁡(a))2)(re⁡(a))2(im⁡(a))2+(4x(x2−(re⁡(a))2+(im⁡(a))2)+1)(x+(x2−(re⁡(a))2+(im⁡(a))2)2−4(re⁡(a))2(im⁡(a))2))3sign⁡3(x+(a2−x2)2)(x+(a2−x2)2)2∣x+(a2−x2)2∣2(x+(a2−x2)2)∣x+(a2−x2)2∣\frac{\frac{4 \left(a^{2} - 3 x^{2}\right) \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{x + \left(a^{2} - x^{2}\right)^{2}} + \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \frac{\partial^{2}}{\partial x^{2}} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + 12 \left(2 x \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 16 x \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + 2 \left(64 x^{2} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right)^{2} + 4 \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 32 \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + \frac{2 \left(4 x \left(a^{2} - x^{2}\right) - 1\right) \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{x + \left(a^{2} - x^{2}\right)^{2}} + \frac{2 \left(4 x \left(a^{2} - x^{2}\right) - 1\right) \left(64 x^{2} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right)^{2} + 4 \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 32 \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{x + \left(a^{2} - x^{2}\right)^{2}} - \frac{3 \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right)^{2} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} \frac{\partial}{\partial x} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|} - \frac{3 \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \left(64 x^{2} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right)^{2} + 4 \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 32 \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{sign}^{2}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|} + \frac{2 \left(4 x \left(a^{2} - x^{2}\right) - 1\right)^{2} \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right)^{2}} - \frac{3 \left(4 x \left(a^{2} - x^{2}\right) - 1\right) \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right)^{2} \operatorname{sign}^{2}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right)^{2} \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|} + \frac{2 \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right)^{3} \operatorname{sign}^{3}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right)^{2} \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|^{2}}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|}
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