Sr Examen

Derivada de y=arctg(x)ln(2x)

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

Gráfico:

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Solución

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