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xlog(4x^2+1)-2x+atan⁡(2x)

Derivada de xlog(4x^2+1)-2x+atan⁡(2x)

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Gráfico:

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Solución

Ha introducido [src]
     /   2    \                  
x*log\4*x  + 1/ - 2*x + atan(2*x)
$$\left(x \log{\left(4 x^{2} + 1 \right)} - 2 x\right) + \operatorname{atan}{\left(2 x \right)}$$
x*log(4*x^2 + 1) - 2*x + atan(2*x)
Gráfica
Primera derivada [src]
                     2                  
        2         8*x         /   2    \
-2 + -------- + -------- + log\4*x  + 1/
            2      2                    
     1 + 4*x    4*x  + 1                
$$\frac{8 x^{2}}{4 x^{2} + 1} + \log{\left(4 x^{2} + 1 \right)} - 2 + \frac{2}{4 x^{2} + 1}$$
Segunda derivada [src]
    /                    2  \
    |       2         8*x   |
8*x*|3 - -------- - --------|
    |           2          2|
    \    1 + 4*x    1 + 4*x /
-----------------------------
                  2          
           1 + 4*x           
$$\frac{8 x \left(- \frac{8 x^{2}}{4 x^{2} + 1} + 3 - \frac{2}{4 x^{2} + 1}\right)}{4 x^{2} + 1}$$
Tercera derivada [src]
  /                    2            2              4  \
  |       2        48*x         32*x          128*x   |
8*|3 - -------- - -------- + ----------- + -----------|
  |           2          2             2             2|
  |    1 + 4*x    1 + 4*x    /       2\    /       2\ |
  \                          \1 + 4*x /    \1 + 4*x / /
-------------------------------------------------------
                               2                       
                        1 + 4*x                        
$$\frac{8 \left(\frac{128 x^{4}}{\left(4 x^{2} + 1\right)^{2}} - \frac{48 x^{2}}{4 x^{2} + 1} + \frac{32 x^{2}}{\left(4 x^{2} + 1\right)^{2}} + 3 - \frac{2}{4 x^{2} + 1}\right)}{4 x^{2} + 1}$$
Gráfico
Derivada de xlog(4x^2+1)-2x+atan⁡(2x)