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Derivada de la función/ x^x^3/ x^3+x/ x^x^3+x^3^x+3^x^x

Derivada de x^x^3+x^3^x+3^x^x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
 / 3\    / x\    / x\
 \x /    \3 /    \x /
x     + x     + 3
3xx+(x3x+xx3)3^{x^{x}} + \left(x^{3^{x}} + x^{x^{3}}\right) 
x^(x^3) + x^(3^x) + 3^(x^x)
Solución detallada

  1. diferenciamos 3xx+(x3x+xx3)3^{x^{x}} + \left(x^{3^{x}} + x^{x^{3}}\right) miembro por miembro:

    1. diferenciamos x3x+xx3x^{3^{x}} + x^{x^{3}} miembro por miembro:

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

        Perola derivada

        (log⁡(x3)+1)(x3)x3\left(\log{\left(x^{3} \right)} + 1\right) \left(x^{3}\right)^{x^{3}}

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

        Perola derivada

        33xx(log⁡(3x)+1)3^{3^{x} x} \left(\log{\left(3^{x} \right)} + 1\right)

      Como resultado de: 33xx(log⁡(3x)+1)+(log⁡(x3)+1)(x3)x33^{3^{x} x} \left(\log{\left(3^{x} \right)} + 1\right) + \left(\log{\left(x^{3} \right)} + 1\right) \left(x^{3}\right)^{x^{3}}

    2. Sustituimos u=xxu = x^{x}.

    3. ddu3u=3ulog⁡(3)\frac{d}{d u} 3^{u} = 3^{u} \log{\left(3 \right)}

    4. Luego se aplica una cadena de reglas. Multiplicamos por ddxxx\frac{d}{d x} x^{x}:

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

        Perola derivada

        xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

      Como resultado de la secuencia de reglas:

      3xxxx(log⁡(x)+1)log⁡(3)3^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(3 \right)}

    Como resultado de: 3xxxx(log⁡(x)+1)log⁡(3)+33xx(log⁡(3x)+1)+(log⁡(x3)+1)(x3)x33^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(3 \right)} + 3^{3^{x} x} \left(\log{\left(3^{x} \right)} + 1\right) + \left(\log{\left(x^{3} \right)} + 1\right) \left(x^{3}\right)^{x^{3}}

  2. Simplificamos:

    3xxxx(log⁡(x)+1)log⁡(3)+33xx(xlog⁡(3)+1)+(log⁡(x3)+1)(x3)x33^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(3 \right)} + 3^{3^{x} x} \left(x \log{\left(3 \right)} + 1\right) + \left(\log{\left(x^{3} \right)} + 1\right) \left(x^{3}\right)^{x^{3}}

Respuesta:

3xxxx(log⁡(x)+1)log⁡(3)+33xx(xlog⁡(3)+1)+(log⁡(x3)+1)(x3)x33^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(3 \right)} + 3^{3^{x} x} \left(x \log{\left(3 \right)} + 1\right) + \left(\log{\left(x^{3} \right)} + 1\right) \left(x^{3}\right)^{x^{3}}

Primera derivada [src] 
 / x\ / x                   \    / 3\                       / x\                       
 \3 / |3     x              |    \x / / 2      2       \    \x /  x                    
x    *|-- + 3 *log(3)*log(x)| + x    *\x  + 3*x *log(x)/ + 3    *x *(1 + log(x))*log(3)
      \x                    /
3xxxx(log⁡(x)+1)log⁡(3)+x3x(3xlog⁡(3)log⁡(x)+3xx)+xx3(3x2log⁡(x)+x2)3^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(3 \right)} + x^{3^{x}} \left(3^{x} \log{\left(3 \right)} \log{\left(x \right)} + \frac{3^{x}}{x}\right) + x^{x^{3}} \left(3 x^{2} \log{\left(x \right)} + x^{2}\right)
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Segunda derivada [src] 
                                                                                                                                     / x\                                                                             
   / 3\                      / x\                                            / x\                    2       / 3\                    \x /  x           / x\                            / x\                           
   \x /                   x  \3 / /  1       2             2*log(3)\    2*x  \3 / /1                \     4  \x /               2   3    *x *log(3)    \x /  x             2           \x /  2*x             2    2   
x*x    *(5 + 6*log(x)) + 3 *x    *|- -- + log (3)*log(x) + --------| + 3   *x    *|- + log(3)*log(x)|  + x *x    *(1 + 3*log(x))  + --------------- + 3    *x *(1 + log(x)) *log(3) + 3    *x   *(1 + log(x)) *log (3)
                                  |   2                       x    |              \x                /                                      x                                                                          
                                  \  x                             /
32xx3x(log⁡(3)log⁡(x)+1x)2+3xx3x(log⁡(3)2log⁡(x)+2log⁡(3)x−1x2)+3xxx2x(log⁡(x)+1)2log⁡(3)2+3xxxx(log⁡(x)+1)2log⁡(3)+3xxxxlog⁡(3)x+x4xx3(3log⁡(x)+1)2+xxx3(6log⁡(x)+5)3^{2 x} x^{3^{x}} \left(\log{\left(3 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + 3^{x} x^{3^{x}} \left(\log{\left(3 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(3 \right)}}{x} - \frac{1}{x^{2}}\right) + 3^{x^{x}} x^{2 x} \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(3 \right)}^{2} + 3^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(3 \right)} + \frac{3^{x^{x}} x^{x} \log{\left(3 \right)}}{x} + x^{4} x^{x^{3}} \left(3 \log{\left(x \right)} + 1\right)^{2} + x x^{x^{3}} \left(6 \log{\left(x \right)} + 5\right)
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Tercera derivada [src] 
                                                                                                                                                                                                                 / x\                                                                                                                                                                      / x\                             / x\                          
 / 3\                       / x\ /                                      2   \         / x\                    3       / 3\                    / x\                            / x\                               \x /  x             / x\                                      / x\                                                                / 3\                                    \x /  x                          \x /  2*x    2                
 \x /                    x  \3 / |2       3             3*log(3)   3*log (3)|    3*x  \3 / /1                \     6  \x /               3    \x /  x             3           \x /  3*x             3    3      3    *x *log(3)      \x /  2*x             3    2         2*x  \3 / /1                \ /  1       2             2*log(3)\      3  \x /                                 3*3    *x *(1 + log(x))*log(3)   3*3    *x   *log (3)*(1 + log(x))
x    *(11 + 6*log(x)) + 3 *x    *|-- + log (3)*log(x) - -------- + ---------| + 3   *x    *|- + log(3)*log(x)|  + x *x    *(1 + 3*log(x))  + 3    *x *(1 + log(x)) *log(3) + 3    *x   *(1 + log(x)) *log (3) - --------------- + 3*3    *x   *(1 + log(x)) *log (3) + 3*3   *x    *|- + log(3)*log(x)|*|- -- + log (3)*log(x) + --------| + 3*x *x    *(1 + 3*log(x))*(5 + 6*log(x)) + ------------------------------ + ---------------------------------
                                 | 3                        2          x    |              \x                /                                                                                                          2                                                           \x                / |   2                       x    |                                                            x                                  x                
                                 \x                        x                /                                                                                                                                          x                                                                                \  x                             /
33xx3x(log⁡(3)log⁡(x)+1x)3+3⋅32xx3x(log⁡(3)log⁡(x)+1x)(log⁡(3)2log⁡(x)+2log⁡(3)x−1x2)+3xx3x(log⁡(3)3log⁡(x)+3log⁡(3)2x−3log⁡(3)x2+2x3)+3xxx3x(log⁡(x)+1)3log⁡(3)3+3⋅3xxx2x(log⁡(x)+1)3log⁡(3)2+3xxxx(log⁡(x)+1)3log⁡(3)+3⋅3xxx2x(log⁡(x)+1)log⁡(3)2x+3⋅3xxxx(log⁡(x)+1)log⁡(3)x−3xxxxlog⁡(3)x2+x6xx3(3log⁡(x)+1)3+3x3xx3(3log⁡(x)+1)(6log⁡(x)+5)+xx3(6log⁡(x)+11)3^{3 x} x^{3^{x}} \left(\log{\left(3 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 \cdot 3^{2 x} x^{3^{x}} \left(\log{\left(3 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(3 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(3 \right)}}{x} - \frac{1}{x^{2}}\right) + 3^{x} x^{3^{x}} \left(\log{\left(3 \right)}^{3} \log{\left(x \right)} + \frac{3 \log{\left(3 \right)}^{2}}{x} - \frac{3 \log{\left(3 \right)}}{x^{2}} + \frac{2}{x^{3}}\right) + 3^{x^{x}} x^{3 x} \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(3 \right)}^{3} + 3 \cdot 3^{x^{x}} x^{2 x} \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(3 \right)}^{2} + 3^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(3 \right)} + \frac{3 \cdot 3^{x^{x}} x^{2 x} \left(\log{\left(x \right)} + 1\right) \log{\left(3 \right)}^{2}}{x} + \frac{3 \cdot 3^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(3 \right)}}{x} - \frac{3^{x^{x}} x^{x} \log{\left(3 \right)}}{x^{2}} + x^{6} x^{x^{3}} \left(3 \log{\left(x \right)} + 1\right)^{3} + 3 x^{3} x^{x^{3}} \left(3 \log{\left(x \right)} + 1\right) \left(6 \log{\left(x \right)} + 5\right) + x^{x^{3}} \left(6 \log{\left(x \right)} + 11\right)
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