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y=sqrt(arctg^4)*e^x/ln(3x)
Derivada de la función/ arctg/ ln(3x)/ y=sqrt(arctg^4)*e^x/ln(3x)

Derivada de y=sqrt(arctg^4)*e^x/ln(3x)

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

Gráfico:

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Solución

Ha introducido [src] 
   __________   
  /     4      x
\/  atan (x) *E 
----------------
    log(3*x)
exatan⁡4(x)log⁡(3x)\frac{e^{x} \sqrt{\operatorname{atan}^{4}{\left(x \right)}}}{\log{\left(3 x \right)}} 
(sqrt(atan(x)^4)*E^x)/log(3*x)
Gráfica
02468-8-6-4-2-1010-2000020000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                         x              
    2     x   2*atan(x)*e               
atan (x)*e  + ------------              
                      2          2     x
                 1 + x       atan (x)*e 
-------------------------- - -----------
         log(3*x)                 2     
                             x*log (3*x)
exatan⁡2(x)+2exatan⁡(x)x2+1log⁡(3x)−exatan⁡2(x)xlog⁡(3x)2\frac{e^{x} \operatorname{atan}^{2}{\left(x \right)} + \frac{2 e^{x} \operatorname{atan}{\left(x \right)}}{x^{2} + 1}}{\log{\left(3 x \right)}} - \frac{e^{x} \operatorname{atan}^{2}{\left(x \right)}}{x \log{\left(3 x \right)}^{2}}
Simplificar
Segunda derivada [src] 
/                                                                          /  2             \        \   
|                                                  2    /       2    \   2*|------ + atan(x)|*atan(x)|   
|                                              atan (x)*|1 + --------|     |     2          |        |   
|    2      2*(-1 + 2*x*atan(x))   4*atan(x)            \    log(3*x)/     \1 + x           /        |  x
|atan (x) - -------------------- + --------- + ----------------------- - ----------------------------|*e 
|                        2                2           2                           x*log(3*x)         |   
|                /     2\            1 + x           x *log(3*x)                                     |   
\                \1 + x /                                                                            /   
---------------------------------------------------------------------------------------------------------
                                                 log(3*x)
(atan⁡2(x)+4atan⁡(x)x2+1−2(2xatan⁡(x)−1)(x2+1)2−2(atan⁡(x)+2x2+1)atan⁡(x)xlog⁡(3x)+(1+2log⁡(3x))atan⁡2(x)x2log⁡(3x))exlog⁡(3x)\frac{\left(\operatorname{atan}^{2}{\left(x \right)} + \frac{4 \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{2 \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(\operatorname{atan}{\left(x \right)} + \frac{2}{x^{2} + 1}\right) \operatorname{atan}{\left(x \right)}}{x \log{\left(3 x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(3 x \right)}}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{2} \log{\left(3 x \right)}}\right) e^{x}}{\log{\left(3 x \right)}}
Simplificar
Tercera derivada [src] 
/                                    /            2                  \                 /    2      2*(-1 + 2*x*atan(x))   4*atan(x)\                                                                                      \   
|                                    | 3*x     4*x *atan(x)          |               3*|atan (x) - -------------------- + ---------|         2    /       3           3    \     /       2    \ /  2             \        |   
|                                  4*|------ - ------------ + atan(x)|                 |                        2                2 |   2*atan (x)*|1 + -------- + ---------|   3*|1 + --------|*|------ + atan(x)|*atan(x)|   
|                                    |     2           2             |                 |                /     2\            1 + x  |              |    log(3*x)      2     |     \    log(3*x)/ |     2          |        |   
|    2      6*(-1 + 2*x*atan(x))     \1 + x       1 + x              /   6*atan(x)     \                \1 + x /                   /              \               log (3*x)/                    \1 + x           /        |  x
|atan (x) - -------------------- - ----------------------------------- + --------- - ----------------------------------------------- - ------------------------------------- + -------------------------------------------|*e 
|                        2                              2                       2                       x*log(3*x)                                   3                                          2                         |   
|                /     2\                       /     2\                   1 + x                                                                    x *log(3*x)                                x *log(3*x)                |   
\                \1 + x /                       \1 + x /                                                                                                                                                                  /   
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                           log(3*x)
(atan⁡2(x)+6atan⁡(x)x2+1−6(2xatan⁡(x)−1)(x2+1)2−4(−4x2atan⁡(x)x2+1+3xx2+1+atan⁡(x))(x2+1)2−3(atan⁡2(x)+4atan⁡(x)x2+1−2(2xatan⁡(x)−1)(x2+1)2)xlog⁡(3x)+3(1+2log⁡(3x))(atan⁡(x)+2x2+1)atan⁡(x)x2log⁡(3x)−2(1+3log⁡(3x)+3log⁡(3x)2)atan⁡2(x)x3log⁡(3x))exlog⁡(3x)\frac{\left(\operatorname{atan}^{2}{\left(x \right)} + \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{6 \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{4 \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(\operatorname{atan}^{2}{\left(x \right)} + \frac{4 \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{2 \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}}\right)}{x \log{\left(3 x \right)}} + \frac{3 \left(1 + \frac{2}{\log{\left(3 x \right)}}\right) \left(\operatorname{atan}{\left(x \right)} + \frac{2}{x^{2} + 1}\right) \operatorname{atan}{\left(x \right)}}{x^{2} \log{\left(3 x \right)}} - \frac{2 \left(1 + \frac{3}{\log{\left(3 x \right)}} + \frac{3}{\log{\left(3 x \right)}^{2}}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{3} \log{\left(3 x \right)}}\right) e^{x}}{\log{\left(3 x \right)}}
Simplificar
Gráfico
Derivada de y=sqrt(arctg^4)*e^x/ln(3x)
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