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y=arctg3inx/x+2
Derivada de la función/ x/x+2/ arctg/ inx/x/ y=arctg3inx/x+2

Derivada de y=arctg3inx/x+2

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

Gráfico:

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Solución

Ha introducido [src] 
atan(3*log(x))    
-------------- + 2
      x
2+atan⁡(3log⁡(x))x2 + \frac{\operatorname{atan}{\left(3 \log{\left(x \right)} \right)}}{x} 
atan(3*log(x))/x + 2
Gráfica
02468-8-6-4-2-1010-200200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  atan(3*log(x))           3         
- -------------- + ------------------
         2          2 /         2   \
        x          x *\1 + 9*log (x)/
−atan⁡(3log⁡(x))x2+3x2(9log⁡(x)2+1)- \frac{\operatorname{atan}{\left(3 \log{\left(x \right)} \right)}}{x^{2}} + \frac{3}{x^{2} \left(9 \log{\left(x \right)}^{2} + 1\right)}
Simplificar
Segunda derivada [src] 
        9                               54*log(x)    
- ------------- + 2*atan(3*log(x)) - ----------------
           2                                        2
  1 + 9*log (x)                      /         2   \ 
                                     \1 + 9*log (x)/ 
-----------------------------------------------------
                           3                         
                          x
2atan⁡(3log⁡(x))−99log⁡(x)2+1−54log⁡(x)(9log⁡(x)2+1)2x3\frac{2 \operatorname{atan}{\left(3 \log{\left(x \right)} \right)} - \frac{9}{9 \log{\left(x \right)}^{2} + 1} - \frac{54 \log{\left(x \right)}}{\left(9 \log{\left(x \right)}^{2} + 1\right)^{2}}}{x^{3}}
Simplificar
Tercera derivada [src] 
  /                                                                                    2      \
  |         18                                   11           108*log(x)        648*log (x)   |
3*|- ---------------- - 2*atan(3*log(x)) + ------------- + ---------------- + ----------------|
  |                 2                               2                     2                  3|
  |  /         2   \                       1 + 9*log (x)   /         2   \    /         2   \ |
  \  \1 + 9*log (x)/                                       \1 + 9*log (x)/    \1 + 9*log (x)/ /
-----------------------------------------------------------------------------------------------
                                                4                                              
                                               x
3(−2atan⁡(3log⁡(x))+119log⁡(x)2+1+108log⁡(x)(9log⁡(x)2+1)2−18(9log⁡(x)2+1)2+648log⁡(x)2(9log⁡(x)2+1)3)x4\frac{3 \left(- 2 \operatorname{atan}{\left(3 \log{\left(x \right)} \right)} + \frac{11}{9 \log{\left(x \right)}^{2} + 1} + \frac{108 \log{\left(x \right)}}{\left(9 \log{\left(x \right)}^{2} + 1\right)^{2}} - \frac{18}{\left(9 \log{\left(x \right)}^{2} + 1\right)^{2}} + \frac{648 \log{\left(x \right)}^{2}}{\left(9 \log{\left(x \right)}^{2} + 1\right)^{3}}\right)}{x^{4}}
Simplificar
Gráfico
Derivada de y=arctg3inx/x+2
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