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Derivada de la función/ |x|*x^2+sin(x^2)+x/(exp(x)-1)

Derivada de |x|*x^2+sin(x^2)+x/(exp(x)-1)

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

Ha introducido [src] 
     2      / 2\     x   
|x|*x  + sin\x / + ------
                    x    
                   e  - 1
xex−1+(x2∣x∣+sin⁡(x2))\frac{x}{e^{x} - 1} + \left(x^{2} \left|{x}\right| + \sin{\left(x^{2} \right)}\right) 
|x|*x^2 + sin(x^2) + x/(exp(x) - 1)
Primera derivada [src] 
                                                    x  
  1       2                            / 2\      x*e   
------ + x *sign(x) + 2*x*|x| + 2*x*cos\x / - ---------
 x                                                    2
e  - 1                                        / x    \ 
                                              \e  - 1/
x2sign⁡(x)+2xcos⁡(x2)+2x∣x∣−xex(ex−1)2+1ex−1x^{2} \operatorname{sign}{\left(x \right)} + 2 x \cos{\left(x^{2} \right)} + 2 x \left|{x}\right| - \frac{x e^{x}}{\left(e^{x} - 1\right)^{2}} + \frac{1}{e^{x} - 1}
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Segunda derivada [src] 
                                         x                                               x            2*x 
             / 2\      2    / 2\      2*e          2                                  x*e        2*x*e    
2*|x| + 2*cos\x / - 4*x *sin\x / - ---------- + 2*x *DiracDelta(x) + 4*x*sign(x) - ---------- + ----------
                                            2                                               2            3
                                   /      x\                                       /      x\    /      x\ 
                                   \-1 + e /                                       \-1 + e /    \-1 + e /
−4x2sin⁡(x2)+2x2δ(x)+4xsign⁡(x)−xex(ex−1)2+2xe2x(ex−1)3+2cos⁡(x2)+2∣x∣−2ex(ex−1)2- 4 x^{2} \sin{\left(x^{2} \right)} + 2 x^{2} \delta\left(x\right) + 4 x \operatorname{sign}{\left(x \right)} - \frac{x e^{x}}{\left(e^{x} - 1\right)^{2}} + \frac{2 x e^{2 x}}{\left(e^{x} - 1\right)^{3}} + 2 \cos{\left(x^{2} \right)} + 2 \left|{x}\right| - \frac{2 e^{x}}{\left(e^{x} - 1\right)^{2}}
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Tercera derivada [src] 
                                                x                                   2*x                                x            3*x          2*x 
                    / 2\      3    / 2\      3*e          2                      6*e                                x*e        6*x*e        6*x*e    
6*sign(x) - 12*x*sin\x / - 8*x *cos\x / - ---------- + 2*x *DiracDelta(x, 1) + ---------- + 12*x*DiracDelta(x) - ---------- - ---------- + ----------
                                                   2                                    3                                 2            4            3
                                          /      x\                            /      x\                         /      x\    /      x\    /      x\ 
                                          \-1 + e /                            \-1 + e /                         \-1 + e /    \-1 + e /    \-1 + e /
−8x3cos⁡(x2)+2x2δ(1)(x)−12xsin⁡(x2)+12xδ(x)−xex(ex−1)2+6xe2x(ex−1)3−6xe3x(ex−1)4+6sign⁡(x)−3ex(ex−1)2+6e2x(ex−1)3- 8 x^{3} \cos{\left(x^{2} \right)} + 2 x^{2} \delta^{\left( 1 \right)}\left( x \right) - 12 x \sin{\left(x^{2} \right)} + 12 x \delta\left(x\right) - \frac{x e^{x}}{\left(e^{x} - 1\right)^{2}} + \frac{6 x e^{2 x}}{\left(e^{x} - 1\right)^{3}} - \frac{6 x e^{3 x}}{\left(e^{x} - 1\right)^{4}} + 6 \operatorname{sign}{\left(x \right)} - \frac{3 e^{x}}{\left(e^{x} - 1\right)^{2}} + \frac{6 e^{2 x}}{\left(e^{x} - 1\right)^{3}}
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