Sr Examen

Otras calculadoras


x*log(x^2+4)-2*x+4*arctg(x/2)

Derivada de x*log(x^2+4)-2*x+4*arctg(x/2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
     / 2    \               /x\
x*log\x  + 4/ - 2*x + 4*atan|-|
                            \2/
$$\left(x \log{\left(x^{2} + 4 \right)} - 2 x\right) + 4 \operatorname{atan}{\left(\frac{x}{2} \right)}$$
x*log(x^2 + 4) - 2*x + 4*atan(x/2)
Gráfica
Primera derivada [src]
                  2               
       2       2*x        / 2    \
-2 + ------ + ------ + log\x  + 4/
          2    2                  
         x    x  + 4              
     1 + --                       
         4                        
$$\frac{2 x^{2}}{x^{2} + 4} + \log{\left(x^{2} + 4 \right)} - 2 + \frac{2}{\frac{x^{2}}{4} + 1}$$
Segunda derivada [src]
    /                 2 \
    |      8       2*x  |
2*x*|3 - ------ - ------|
    |         2        2|
    \    4 + x    4 + x /
-------------------------
               2         
          4 + x          
$$\frac{2 x \left(- \frac{2 x^{2}}{x^{2} + 4} + 3 - \frac{8}{x^{2} + 4}\right)}{x^{2} + 4}$$
Tercera derivada [src]
  /                 2          4           2  \
  |      8      12*x        8*x        32*x   |
2*|3 - ------ - ------ + --------- + ---------|
  |         2        2           2           2|
  |    4 + x    4 + x    /     2\    /     2\ |
  \                      \4 + x /    \4 + x / /
-----------------------------------------------
                          2                    
                     4 + x                     
$$\frac{2 \left(\frac{8 x^{4}}{\left(x^{2} + 4\right)^{2}} - \frac{12 x^{2}}{x^{2} + 4} + \frac{32 x^{2}}{\left(x^{2} + 4\right)^{2}} + 3 - \frac{8}{x^{2} + 4}\right)}{x^{2} + 4}$$
Gráfico
Derivada de x*log(x^2+4)-2*x+4*arctg(x/2)