Sr Examen

Otras calculadoras

Derivada de la función/ x^x^x/ y=x^x/ x^x^2/ y=x^x^x^2

Derivada de y=x^x^x^2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 / / 2\\
 | \x /|
 \x    /
x
xxx2x^{x^{x^{2}}} 
x^(x^(x^2))
Solución detallada

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

    Perola derivada

    (log⁡(xx2)+1)(xx2)xx2\left(\log{\left(x^{x^{2}} \right)} + 1\right) \left(x^{x^{2}}\right)^{x^{x^{2}}}

Respuesta:

(log⁡(xx2)+1)(xx2)xx2\left(\log{\left(x^{x^{2}} \right)} + 1\right) \left(x^{x^{2}}\right)^{x^{x^{2}}}

Primera derivada [src] 
 / / 2\\ / / 2\                                \
 | \x /| | \x /    / 2\                        |
 \x    / |x        \x /                        |
x       *|----- + x    *(x + 2*x*log(x))*log(x)|
         \  x                                  /
xxx2(xx2(2xlog⁡(x)+x)log⁡(x)+xx2x)x^{x^{x^{2}}} \left(x^{x^{2}} \left(2 x \log{\left(x \right)} + x\right) \log{\left(x \right)} + \frac{x^{x^{2}}}{x}\right)
Simplificar
Segunda derivada [src] 
       / / 2\\                                                                                                               
 / 2\  | \x /| /                     / 2\                              2                                                    \
 \x /  \x    / |    1                \x / /1                          \                             2               2       |
x    *x       *|2 - -- + 4*log(x) + x    *|- + x*(1 + 2*log(x))*log(x)|  + (3 + 2*log(x))*log(x) + x *(1 + 2*log(x)) *log(x)|
               |     2                    \x                          /                                                     |
               \    x                                                                                                       /
xx2xxx2(x2(2log⁡(x)+1)2log⁡(x)+xx2(x(2log⁡(x)+1)log⁡(x)+1x)2+(2log⁡(x)+3)log⁡(x)+4log⁡(x)+2−1x2)x^{x^{2}} x^{x^{x^{2}}} \left(x^{2} \left(2 \log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + x^{x^{2}} \left(x \left(2 \log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \left(2 \log{\left(x \right)} + 3\right) \log{\left(x \right)} + 4 \log{\left(x \right)} + 2 - \frac{1}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
       / / 2\\                                                                                                                                                                                                                                                                                                          
 / 2\  | \x /| /         2                              3                                                                                                         / 2\                                                                                                                                                 \
 \x /  \x    / |2     2*x  /1                          \    3*(1 + 2*log(x))   2*log(x)                     2   3*(3 + 2*log(x))    3               3             \x / /1                          \ /    1                                        2               2       \                                           |
x    *x       *|-- + x    *|- + x*(1 + 2*log(x))*log(x)|  - ---------------- + -------- + 3*x*(1 + 2*log(x))  + ---------------- + x *(1 + 2*log(x)) *log(x) + 3*x    *|- + x*(1 + 2*log(x))*log(x)|*|2 - -- + 4*log(x) + (3 + 2*log(x))*log(x) + x *(1 + 2*log(x)) *log(x)| + 3*x*(1 + 2*log(x))*(3 + 2*log(x))*log(x)|
               | 3         \x                          /           x              x                                    x                                               \x                          / |     2                                                               |                                           |
               \x                                                                                                                                                                                    \    x                                                                /                                           /
xx2xxx2(x3(2log⁡(x)+1)3log⁡(x)+3x(2log⁡(x)+1)2+3x(2log⁡(x)+1)(2log⁡(x)+3)log⁡(x)+x2x2(x(2log⁡(x)+1)log⁡(x)+1x)3+3xx2(x(2log⁡(x)+1)log⁡(x)+1x)(x2(2log⁡(x)+1)2log⁡(x)+(2log⁡(x)+3)log⁡(x)+4log⁡(x)+2−1x2)−3(2log⁡(x)+1)x+3(2log⁡(x)+3)x+2log⁡(x)x+2x3)x^{x^{2}} x^{x^{x^{2}}} \left(x^{3} \left(2 \log{\left(x \right)} + 1\right)^{3} \log{\left(x \right)} + 3 x \left(2 \log{\left(x \right)} + 1\right)^{2} + 3 x \left(2 \log{\left(x \right)} + 1\right) \left(2 \log{\left(x \right)} + 3\right) \log{\left(x \right)} + x^{2 x^{2}} \left(x \left(2 \log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{x^{2}} \left(x \left(2 \log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(x^{2} \left(2 \log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \left(2 \log{\left(x \right)} + 3\right) \log{\left(x \right)} + 4 \log{\left(x \right)} + 2 - \frac{1}{x^{2}}\right) - \frac{3 \left(2 \log{\left(x \right)} + 1\right)}{x} + \frac{3 \left(2 \log{\left(x \right)} + 3\right)}{x} + \frac{2 \log{\left(x \right)}}{x} + \frac{2}{x^{3}}\right)
Simplificar
    © Sr Examen – Калькулятор