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y=log(x,5)^x^2
Derivada de la función/ y=log/ y=log(x,5)^x^2

Derivada de y=log(x,5)^x^2

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

Gráfico:

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Solución

Ha introducido [src] 
        / 2\
        \x /
/log(x)\    
|------|    
\log(5)/
(log⁡(x)log⁡(5))x2\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)^{x^{2}} 
(log(x)/log(5))^(x^2)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(x2)+1)∣x∣2x2\left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}}

Respuesta:

(log⁡(x2)+1)∣x∣2x2\left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}}

Gráfica
02468-8-6-4-2-1010-5000000000000000050000000000000000
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Primera derivada [src] 
        / 2\                           
        \x /                           
/log(x)\     /  x             /log(x)\\
|------|    *|------ + 2*x*log|------||
\log(5)/     \log(x)          \log(5)//
(log⁡(x)log⁡(5))x2(2xlog⁡(log⁡(x)log⁡(5))+xlog⁡(x))\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)^{x^{2}} \left(2 x \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{x}{\log{\left(x \right)}}\right)
Simplificar
Segunda derivada [src] 
        / 2\                                                                    
        \x / /                                                                2\
/log(x)\     |     1           /log(x)\     3       2 /  1           /log(x)\\ |
|------|    *|- ------- + 2*log|------| + ------ + x *|------ + 2*log|------|| |
\log(5)/     |     2           \log(5)/   log(x)      \log(x)        \log(5)// |
             \  log (x)                                                        /
(log⁡(x)log⁡(5))x2(x2(2log⁡(log⁡(x)log⁡(5))+1log⁡(x))2+2log⁡(log⁡(x)log⁡(5))+3log⁡(x)−1log⁡(x)2)\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)^{x^{2}} \left(x^{2} \left(2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} + 2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{3}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right)
Simplificar
Tercera derivada [src] 
             /                                     3         2                                                                       \
        / 2\ |                               2 - ------ + -------                                                                    |
        \x / |                           3       log(x)      2                                                                       |
/log(x)\     | 3 /  1           /log(x)\\                 log (x)       /  1           /log(x)\\ /     1           /log(x)\     3   \|
|------|    *|x *|------ + 2*log|------||  + -------------------- + 3*x*|------ + 2*log|------||*|- ------- + 2*log|------| + ------||
\log(5)/     |   \log(x)        \log(5)//          x*log(x)             \log(x)        \log(5)// |     2           \log(5)/   log(x)||
             \                                                                                   \  log (x)                         //
(log⁡(x)log⁡(5))x2(x3(2log⁡(log⁡(x)log⁡(5))+1log⁡(x))3+3x(2log⁡(log⁡(x)log⁡(5))+1log⁡(x))(2log⁡(log⁡(x)log⁡(5))+3log⁡(x)−1log⁡(x)2)+2−3log⁡(x)+2log⁡(x)2xlog⁡(x))\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)^{x^{2}} \left(x^{3} \left(2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + 3 x \left(2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{1}{\log{\left(x \right)}}\right) \left(2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{3}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right) + \frac{2 - \frac{3}{\log{\left(x \right)}} + \frac{2}{\log{\left(x \right)}^{2}}}{x \log{\left(x \right)}}\right)
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Gráfico
Derivada de y=log(x,5)^x^2
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