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Derivada de la función/ 1+x^2/ |x|sin⁡x+1/(1+x^2)+tan⁡x/x

Derivada de |x|sin⁡x+1/(1+x^2)+tan⁡x/x

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

Gráfico:

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Solución

Ha introducido [src] 
               1      tan(x)
|x|*sin(x) + ------ + ------
                  2     x   
             1 + x
(sin⁡(x)∣x∣+1x2+1)+tan⁡(x)x\left(\sin{\left(x \right)} \left|{x}\right| + \frac{1}{x^{2} + 1}\right) + \frac{\tan{\left(x \right)}}{x} 
|x|*sin(x) + 1/(1 + x^2) + tan(x)/x
Primera derivada [src] 
       2                                                      
1 + tan (x)                                 tan(x)      2*x   
----------- + |x|*cos(x) + sign(x)*sin(x) - ------ - ---------
     x                                         2             2
                                              x      /     2\ 
                                                     \1 + x /
−2x(x2+1)2+sin⁡(x)sign⁡(x)+cos⁡(x)∣x∣+tan⁡2(x)+1x−tan⁡(x)x2- \frac{2 x}{\left(x^{2} + 1\right)^{2}} + \sin{\left(x \right)} \operatorname{sign}{\left(x \right)} + \cos{\left(x \right)} \left|{x}\right| + \frac{\tan^{2}{\left(x \right)} + 1}{x} - \frac{\tan{\left(x \right)}}{x^{2}}
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Segunda derivada [src] 
                             /       2   \                                                                2       /       2   \       
      2                    2*\1 + tan (x)/   2*tan(x)                                                  8*x      2*\1 + tan (x)/*tan(x)
- --------- - |x|*sin(x) - --------------- + -------- + 2*DiracDelta(x)*sin(x) + 2*cos(x)*sign(x) + --------- + ----------------------
          2                        2             3                                                          3             x           
  /     2\                        x             x                                                   /     2\                          
  \1 + x /                                                                                          \1 + x /
8x2(x2+1)3−sin⁡(x)∣x∣+2sin⁡(x)δ(x)+2cos⁡(x)sign⁡(x)−2(x2+1)2+2(tan⁡2(x)+1)tan⁡(x)x−2(tan⁡2(x)+1)x2+2tan⁡(x)x3\frac{8 x^{2}}{\left(x^{2} + 1\right)^{3}} - \sin{\left(x \right)} \left|{x}\right| + 2 \sin{\left(x \right)} \delta\left(x\right) + 2 \cos{\left(x \right)} \operatorname{sign}{\left(x \right)} - \frac{2}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(x \right)}}{x^{3}}
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Tercera derivada [src] 
                                                                       2                                                                                                                                      
                    3                                     /       2   \                                  /       2   \                                          /       2   \               2    /       2   \
                48*x      6*tan(x)                      2*\1 + tan (x)/                                6*\1 + tan (x)/                               24*x     6*\1 + tan (x)/*tan(x)   4*tan (x)*\1 + tan (x)/
-|x|*cos(x) - --------- - -------- - 3*sign(x)*sin(x) + ---------------- + 2*DiracDelta(x, 1)*sin(x) + --------------- + 6*DiracDelta(x)*cos(x) + --------- - ---------------------- + -----------------------
                      4       4                                x                                               3                                          3              2                        x           
              /     2\       x                                                                                x                                   /     2\              x                                     
              \1 + x /                                                                                                                            \1 + x /
−48x3(x2+1)4+24x(x2+1)3+2sin⁡(x)δ(1)(x)−3sin⁡(x)sign⁡(x)−cos⁡(x)∣x∣+6cos⁡(x)δ(x)+2(tan⁡2(x)+1)2x+4(tan⁡2(x)+1)tan⁡2(x)x−6(tan⁡2(x)+1)tan⁡(x)x2+6(tan⁡2(x)+1)x3−6tan⁡(x)x4- \frac{48 x^{3}}{\left(x^{2} + 1\right)^{4}} + \frac{24 x}{\left(x^{2} + 1\right)^{3}} + 2 \sin{\left(x \right)} \delta^{\left( 1 \right)}\left( x \right) - 3 \sin{\left(x \right)} \operatorname{sign}{\left(x \right)} - \cos{\left(x \right)} \left|{x}\right| + 6 \cos{\left(x \right)} \delta\left(x\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{x} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{x} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{3}} - \frac{6 \tan{\left(x \right)}}{x^{4}}
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