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x^(ln(2x))+arctg(1/x^5)
Derivada de la función/ 1/x^5/ arctg/ x^(ln(2x))/ x^(ln(2x))+arctg(1/x^5)

Derivada de x^(ln(2x))+arctg(1/x^5)

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

Gráfico:

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Solución

Ha introducido [src] 
 log(2*x)       /1 \
x         + atan|--|
                | 5|
                \x /
xlog⁡(2x)+atan⁡(1x5)x^{\log{\left(2 x \right)}} + \operatorname{atan}{\left(\frac{1}{x^{5}} \right)} 
x^log(2*x) + atan(1/(x^5))
Gráfica
02468-8-6-4-2-1010-25002500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 log(2*x) /log(x)   log(2*x)\        5      
x        *|------ + --------| - ------------
          \  x         x    /    6 /     1 \
                                x *|1 + ---|
                                   |     10|
                                   \    x  /
xlog⁡(2x)(log⁡(x)x+log⁡(2x)x)−5x6(1+1x10)x^{\log{\left(2 x \right)}} \left(\frac{\log{\left(x \right)}}{x} + \frac{\log{\left(2 x \right)}}{x}\right) - \frac{5}{x^{6} \left(1 + \frac{1}{x^{10}}\right)}
Simplificar
Segunda derivada [src] 
 log(2*x)                    2    log(2*x)                                  50              30     
x        *(log(x) + log(2*x))  - x        *(-2 + log(x) + log(2*x)) - -------------- + ------------
                                                                                   2    5 /     1 \
                                                                       15 /     1 \    x *|1 + ---|
                                                                      x  *|1 + ---|       |     10|
                                                                          |     10|       \    x  /
                                                                          \    x  /                
---------------------------------------------------------------------------------------------------
                                                  2                                                
                                                 x
xlog⁡(2x)(log⁡(x)+log⁡(2x))2−xlog⁡(2x)(log⁡(x)+log⁡(2x)−2)+30x5(1+1x10)−50x15(1+1x10)2x2\frac{x^{\log{\left(2 x \right)}} \left(\log{\left(x \right)} + \log{\left(2 x \right)}\right)^{2} - x^{\log{\left(2 x \right)}} \left(\log{\left(x \right)} + \log{\left(2 x \right)} - 2\right) + \frac{30}{x^{5} \left(1 + \frac{1}{x^{10}}\right)} - \frac{50}{x^{15} \left(1 + \frac{1}{x^{10}}\right)^{2}}}{x^{2}}
Simplificar
Tercera derivada [src] 
 log(2*x)                    3        1000            210           log(2*x)                                 1150           log(2*x)                                             
x        *(log(x) + log(2*x))  - -------------- - ------------ + 2*x        *(-3 + log(x) + log(2*x)) + -------------- - 3*x        *(log(x) + log(2*x))*(-2 + log(x) + log(2*x))
                                              3    5 /     1 \                                                       2                                                           
                                  25 /     1 \    x *|1 + ---|                                           15 /     1 \                                                            
                                 x  *|1 + ---|       |     10|                                          x  *|1 + ---|                                                            
                                     |     10|       \    x  /                                              |     10|                                                            
                                     \    x  /                                                              \    x  /                                                            
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                         3                                                                                       
                                                                                        x
xlog⁡(2x)(log⁡(x)+log⁡(2x))3−3xlog⁡(2x)(log⁡(x)+log⁡(2x))(log⁡(x)+log⁡(2x)−2)+2xlog⁡(2x)(log⁡(x)+log⁡(2x)−3)−210x5(1+1x10)+1150x15(1+1x10)2−1000x25(1+1x10)3x3\frac{x^{\log{\left(2 x \right)}} \left(\log{\left(x \right)} + \log{\left(2 x \right)}\right)^{3} - 3 x^{\log{\left(2 x \right)}} \left(\log{\left(x \right)} + \log{\left(2 x \right)}\right) \left(\log{\left(x \right)} + \log{\left(2 x \right)} - 2\right) + 2 x^{\log{\left(2 x \right)}} \left(\log{\left(x \right)} + \log{\left(2 x \right)} - 3\right) - \frac{210}{x^{5} \left(1 + \frac{1}{x^{10}}\right)} + \frac{1150}{x^{15} \left(1 + \frac{1}{x^{10}}\right)^{2}} - \frac{1000}{x^{25} \left(1 + \frac{1}{x^{10}}\right)^{3}}}{x^{3}}
Simplificar
Gráfico
Derivada de x^(ln(2x))+arctg(1/x^5)
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