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y=2x*arctg(x)+lnx^3

Derivada de y=2x*arctg(x)+lnx^3

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

Ha introducido [src]
                 3   
2*x*atan(x) + log (x)
$$2 x \operatorname{atan}{\left(x \right)} + \log{\left(x \right)}^{3}$$
(2*x)*atan(x) + log(x)^3
Gráfica
Primera derivada [src]
                          2   
             2*x     3*log (x)
2*atan(x) + ------ + ---------
                 2       x    
            1 + x             
$$\frac{2 x}{x^{2} + 1} + 2 \operatorname{atan}{\left(x \right)} + \frac{3 \log{\left(x \right)}^{2}}{x}$$
Segunda derivada [src]
               2          2              
  4         4*x      3*log (x)   6*log(x)
------ - --------- - --------- + --------
     2           2        2          2   
1 + x    /     2\        x          x    
         \1 + x /                        
$$- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{4}{x^{2} + 1} - \frac{3 \log{\left(x \right)}^{2}}{x^{2}} + \frac{6 \log{\left(x \right)}}{x^{2}}$$
Tercera derivada [src]
  /                                 2            3  \
  |3    9*log(x)      8*x      3*log (x)      8*x   |
2*|-- - -------- - --------- + --------- + ---------|
  | 3       3              2        3              3|
  |x       x       /     2\        x       /     2\ |
  \                \1 + x /                \1 + x / /
$$2 \left(\frac{8 x^{3}}{\left(x^{2} + 1\right)^{3}} - \frac{8 x}{\left(x^{2} + 1\right)^{2}} + \frac{3 \log{\left(x \right)}^{2}}{x^{3}} - \frac{9 \log{\left(x \right)}}{x^{3}} + \frac{3}{x^{3}}\right)$$
Gráfico
Derivada de y=2x*arctg(x)+lnx^3