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y=(log10x)^x²
Derivada de la función/ log10/ y=(log10x)^x²

Derivada de y=(log10x)^x²

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

Ha introducido [src] 
           / 2\
           \x /
(log(10*x))
$$\log{\left(10 x \right)}^{x^{2}}$$ 
log(10*x)^(x^2)
Solución detallada

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

    Perola derivada

Respuesta:

Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
           / 2\                                 
           \x / /    x                         \
(log(10*x))    *|--------- + 2*x*log(log(10*x))|
                \log(10*x)                     /
$$\left(2 x \log{\left(\log{\left(10 x \right)} \right)} + \frac{x}{\log{\left(10 x \right)}}\right) \log{\left(10 x \right)}^{x^{2}}$$
Simplificar
Segunda derivada [src] 
           / 2\ /                                                                               2\
           \x / |      1                               3        2 /    1                       \ |
(log(10*x))    *|- ---------- + 2*log(log(10*x)) + --------- + x *|--------- + 2*log(log(10*x))| |
                |     2                            log(10*x)      \log(10*x)                   / |
                \  log (10*x)                                                                    /
$$\left(x^{2} \left(2 \log{\left(\log{\left(10 x \right)} \right)} + \frac{1}{\log{\left(10 x \right)}}\right)^{2} + 2 \log{\left(\log{\left(10 x \right)} \right)} + \frac{3}{\log{\left(10 x \right)}} - \frac{1}{\log{\left(10 x \right)}^{2}}\right) \log{\left(10 x \right)}^{x^{2}}$$
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Tercera derivada [src] 
                /                                             3           2                                                                                        \
                |                                     2 - --------- + ----------                                                                                   |
           / 2\ |                                 3       log(10*x)      2                                                                                         |
           \x / | 3 /    1                       \                    log (10*x)       /    1                       \ /      1                               3    \|
(log(10*x))    *|x *|--------- + 2*log(log(10*x))|  + -------------------------- + 3*x*|--------- + 2*log(log(10*x))|*|- ---------- + 2*log(log(10*x)) + ---------||
                |   \log(10*x)                   /           x*log(10*x)               \log(10*x)                   / |     2                            log(10*x)||
                \                                                                                                     \  log (10*x)                               //
$$\left(x^{3} \left(2 \log{\left(\log{\left(10 x \right)} \right)} + \frac{1}{\log{\left(10 x \right)}}\right)^{3} + 3 x \left(2 \log{\left(\log{\left(10 x \right)} \right)} + \frac{1}{\log{\left(10 x \right)}}\right) \left(2 \log{\left(\log{\left(10 x \right)} \right)} + \frac{3}{\log{\left(10 x \right)}} - \frac{1}{\log{\left(10 x \right)}^{2}}\right) + \frac{2 - \frac{3}{\log{\left(10 x \right)}} + \frac{2}{\log{\left(10 x \right)}^{2}}}{x \log{\left(10 x \right)}}\right) \log{\left(10 x \right)}^{x^{2}}$$
Simplificar
Gráfico
Derivada de y=(log10x)^x²
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