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x/(x*lnx^3)
Derivada de la función/ x*lnx/ lnx^3/ x/(x*lnx^3)

Derivada de x/(x*lnx^3)

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

Gráfico:

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Solución

Ha introducido [src] 
    x    
---------
     3   
x*log (x)
xxlog⁡(x)3\frac{x}{x \log{\left(x \right)}^{3}} 
x/((x*log(x)^3))
Gráfica
02468-8-6-4-2-1010-5000050000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                 3           2   
    1       - log (x) - 3*log (x)
--------- + ---------------------
     3                 6         
x*log (x)         x*log (x)
1xlog⁡(x)3+−log⁡(x)3−3log⁡(x)2xlog⁡(x)6\frac{1}{x \log{\left(x \right)}^{3}} + \frac{- \log{\left(x \right)}^{3} - 3 \log{\left(x \right)}^{2}}{x \log{\left(x \right)}^{6}}
Simplificar
Segunda derivada [src] 
              /      3   \                3*(2 + log(x))   3*(3 + log(x))
-3 - log(x) + |1 + ------|*(3 + log(x)) - -------------- + --------------
              \    log(x)/                    log(x)           log(x)    
-------------------------------------------------------------------------
                                 2    4                                  
                                x *log (x)
(1+3log⁡(x))(log⁡(x)+3)−3(log⁡(x)+2)log⁡(x)+3(log⁡(x)+3)log⁡(x)−log⁡(x)−3x2log⁡(x)4\frac{\left(1 + \frac{3}{\log{\left(x \right)}}\right) \left(\log{\left(x \right)} + 3\right) - \frac{3 \left(\log{\left(x \right)} + 2\right)}{\log{\left(x \right)}} + \frac{3 \left(\log{\left(x \right)} + 3\right)}{\log{\left(x \right)}} - \log{\left(x \right)} - 3}{x^{2} \log{\left(x \right)}^{4}}
Simplificar
Tercera derivada [src] 
                                                                                                                                                /      3   \                  /      3   \             
                                                                                                           /        2   \                     3*|1 + ------|*(3 + log(x))   3*|1 + ------|*(2 + log(x))
               /      9         12  \   21*(3 + log(x))   6*(3 + log(x))     /      3   \                3*\-2 + log (x)/   27*(2 + log(x))     \    log(x)/                  \    log(x)/             
- (3 + log(x))*|2 + ------ + -------| - --------------- - -------------- + 2*|1 + ------|*(3 + log(x)) + ---------------- + --------------- - --------------------------- + ---------------------------
               |    log(x)      2   |          2              log(x)         \    log(x)/                       2                  2                     log(x)                        log(x)          
               \             log (x)/       log (x)                                                          log (x)            log (x)                                                                
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                3    4                                                                                                 
                                                                                               x *log (x)
3(1+3log⁡(x))(log⁡(x)+2)log⁡(x)+2(1+3log⁡(x))(log⁡(x)+3)−3(1+3log⁡(x))(log⁡(x)+3)log⁡(x)+27(log⁡(x)+2)log⁡(x)2−(log⁡(x)+3)(2+9log⁡(x)+12log⁡(x)2)−6(log⁡(x)+3)log⁡(x)−21(log⁡(x)+3)log⁡(x)2+3(log⁡(x)2−2)log⁡(x)2x3log⁡(x)4\frac{\frac{3 \left(1 + \frac{3}{\log{\left(x \right)}}\right) \left(\log{\left(x \right)} + 2\right)}{\log{\left(x \right)}} + 2 \left(1 + \frac{3}{\log{\left(x \right)}}\right) \left(\log{\left(x \right)} + 3\right) - \frac{3 \left(1 + \frac{3}{\log{\left(x \right)}}\right) \left(\log{\left(x \right)} + 3\right)}{\log{\left(x \right)}} + \frac{27 \left(\log{\left(x \right)} + 2\right)}{\log{\left(x \right)}^{2}} - \left(\log{\left(x \right)} + 3\right) \left(2 + \frac{9}{\log{\left(x \right)}} + \frac{12}{\log{\left(x \right)}^{2}}\right) - \frac{6 \left(\log{\left(x \right)} + 3\right)}{\log{\left(x \right)}} - \frac{21 \left(\log{\left(x \right)} + 3\right)}{\log{\left(x \right)}^{2}} + \frac{3 \left(\log{\left(x \right)}^{2} - 2\right)}{\log{\left(x \right)}^{2}}}{x^{3} \log{\left(x \right)}^{4}}
Simplificar
Gráfico
Derivada de x/(x*lnx^3)
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