Sr Examen

Derivada de x*exp(-x)arctg(ln(x))+ln(arctg(x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
   -x                            
x*e  *atan(log(x)) + log(atan(x))
$$x e^{- x} \operatorname{atan}{\left(\log{\left(x \right)} \right)} + \log{\left(\operatorname{atan}{\left(x \right)} \right)}$$
(x*exp(-x))*atan(log(x)) + log(atan(x))
Gráfica
Primera derivada [src]
                        -x                                   
       1               e         /     -x    -x\             
---------------- + ----------- + \- x*e   + e  /*atan(log(x))
/     2\                  2                                  
\1 + x /*atan(x)   1 + log (x)                               
$$\left(- x e^{- x} + e^{- x}\right) \operatorname{atan}{\left(\log{\left(x \right)} \right)} + \frac{e^{- x}}{\log{\left(x \right)}^{2} + 1} + \frac{1}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}$$
Segunda derivada [src]
                            -x                                                                   -x         -x         
          1                e                                -x          2*x            (-1 + x)*e        2*e  *log(x)  
- ------------------ - ----------- + (-2 + x)*atan(log(x))*e   - ----------------- - --------------- - ----------------
          2                   2                                          2             /       2   \                  2
  /     2\      2      1 + log (x)                               /     2\            x*\1 + log (x)/     /       2   \ 
  \1 + x / *atan (x)                                             \1 + x / *atan(x)                     x*\1 + log (x)/ 
$$- \frac{2 x}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \left(x - 2\right) e^{- x} \operatorname{atan}{\left(\log{\left(x \right)} \right)} - \frac{e^{- x}}{\log{\left(x \right)}^{2} + 1} - \frac{1}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} - \frac{\left(x - 1\right) e^{- x}}{x \left(\log{\left(x \right)}^{2} + 1\right)} - \frac{2 e^{- x} \log{\left(x \right)}}{x \left(\log{\left(x \right)}^{2} + 1\right)^{2}}$$
Tercera derivada [src]
     -x                                                                                     -x                                        2                     -x                  -x         -x                 -x                   2     -x                 -x       
    e                 2                   2                                   -x         2*e                  6*x                  8*x            (-1 + x)*e        2*(-2 + x)*e        2*e  *log(x)       4*e  *log(x)       8*log (x)*e       2*(-1 + x)*e  *log(x)
----------- - ----------------- + ------------------ - (-3 + x)*atan(log(x))*e   - ----------------- + ------------------ + ----------------- + ---------------- + --------------- + ----------------- + ---------------- + ----------------- + ---------------------
       2              2                   3                                                        2           3                    3            2 /       2   \     /       2   \                   2                  2                   3                     2  
1 + log (x)   /     2\            /     2\      3                                   2 /       2   \    /     2\      2      /     2\            x *\1 + log (x)/   x*\1 + log (x)/    2 /       2   \      /       2   \     2 /       2   \       2 /       2   \   
              \1 + x / *atan(x)   \1 + x / *atan (x)                               x *\1 + log (x)/    \1 + x / *atan (x)   \1 + x / *atan(x)                                        x *\1 + log (x)/    x*\1 + log (x)/    x *\1 + log (x)/      x *\1 + log (x)/   
$$\frac{8 x^{2}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}{\left(x \right)}} + \frac{6 x}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(x \right)}} - \left(x - 3\right) e^{- x} \operatorname{atan}{\left(\log{\left(x \right)} \right)} + \frac{e^{- x}}{\log{\left(x \right)}^{2} + 1} - \frac{2}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{2}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(x \right)}} + \frac{2 \left(x - 2\right) e^{- x}}{x \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{4 e^{- x} \log{\left(x \right)}}{x \left(\log{\left(x \right)}^{2} + 1\right)^{2}} + \frac{\left(x - 1\right) e^{- x}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{2 \left(x - 1\right) e^{- x} \log{\left(x \right)}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)^{2}} + \frac{2 e^{- x} \log{\left(x \right)}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)^{2}} - \frac{2 e^{- x}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)^{2}} + \frac{8 e^{- x} \log{\left(x \right)}^{2}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)^{3}}$$
Gráfico
Derivada de x*exp(-x)arctg(ln(x))+ln(arctg(x))