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y=(x+lnx)*arctgx
Derivada de la función/ x+lnx/ arctg/ y=(x+lnx)*arctgx

Derivada de y=(x+lnx)*arctgx

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

Ha introducido [src] 
(x + log(x))*acot(x)
(x+log⁡(x))acot⁡(x)\left(x + \log{\left(x \right)}\right) \operatorname{acot}{\left(x \right)} 
(x + log(x))*acot(x)
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/    1\           x + log(x)
|1 + -|*acot(x) - ----------
\    x/                  2  
                    1 + x
(1+1x)acot⁡(x)−x+log⁡(x)x2+1\left(1 + \frac{1}{x}\right) \operatorname{acot}{\left(x \right)} - \frac{x + \log{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
              /    1\                   
            2*|1 + -|                   
  acot(x)     \    x/   2*x*(x + log(x))
- ------- - --------- + ----------------
      2            2               2    
     x        1 + x        /     2\     
                           \1 + x /
2x(x+log⁡(x))(x2+1)2−2(1+1x)x2+1−acot⁡(x)x2\frac{2 x \left(x + \log{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(1 + \frac{1}{x}\right)}{x^{2} + 1} - \frac{\operatorname{acot}{\left(x \right)}}{x^{2}}
Simplificar
Tercera derivada [src] 
                            /         2 \                           
                            |      4*x  |                           
                          2*|-1 + ------|*(x + log(x))       /    1\
                            |          2|                6*x*|1 + -|
2*acot(x)        3          \     1 + x /                    \    x/
--------- + ----------- - ---------------------------- + -----------
     3       2 /     2\                    2                      2 
    x       x *\1 + x /            /     2\               /     2\  
                                   \1 + x /               \1 + x /
6x(1+1x)(x2+1)2−2(x+log⁡(x))(4x2x2+1−1)(x2+1)2+3x2(x2+1)+2acot⁡(x)x3\frac{6 x \left(1 + \frac{1}{x}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(x + \log{\left(x \right)}\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{acot}{\left(x \right)}}{x^{3}}
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Gráfico
Derivada de y=(x+lnx)*arctgx
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