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Expresiones idénticas
- x^x^x^x^x
- x en el grado x en el grado x en el grado x en el grado x
- xxxxx
Derivada de x^x^x^x^x
Solución
Solución detallada
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Perola derivada
Respuesta:
Primera derivada
[src]
/ / / x\\\ / / / x\\ \
| | \x /|| | | \x /| / / x\\ / / x\ \ |
| \x /| | \x / | \x /| | \x / / x\ / x \ | |
\x / |x \x / |x \x / |x x | | |
x *|-------- + x *|----- + x *|-- + x *(1 + log(x))*log(x)|*log(x)|*log(x)|
\ x \ x \x / / /
$$x^{x^{x^{x^{x}}}} \left(x^{x^{x^{x}}} \left(x^{x^{x}} \left(x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{x^{x}}{x}\right) \log{\left(x \right)} + \frac{x^{x^{x}}}{x}\right) \log{\left(x \right)} + \frac{x^{x^{x^{x}}}}{x}\right)$$
Segunda derivada
[src]
/ / / x\\\ / / x\ \
/ / x\\ | | \x /|| | / / x\\ 2 / x /1 \\ \x / /1 x /1 \ \|
| \x /| | \x /| | | \x /| / / x\ \ / x\ | 2 2*x *|- + (1 + log(x))*log(x)|| x 2 2*x *|- + x *|- + (1 + log(x))*log(x)|*log(x)||
\x / \x / | 1 \x / |1 \x / /1 x /1 \ \ | \x / | 1 x / 1 log(x) 2 2*(1 + log(x))\ 2*x /1 \ \x /| 2*x /1 x /1 \ \ \x \x / /|
x *x *|- -- + x *|- + x *|- + x *|- + (1 + log(x))*log(x)|*log(x)|*log(x)| + x *|- -- + x *|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x) + x *|- + (1 + log(x))*log(x)| *log(x) + ------------------------------|*log(x) + x *|- + x *|- + (1 + log(x))*log(x)|*log(x)| *log(x) + -------------------------------------------------|
| 2 \x \x \x / / / | 2 | 2 x x | \x / x | \x \x / / x |
\ x \ x \ x / / /
$$x^{x^{x^{x}}} x^{x^{x^{x^{x}}}} \left(x^{2 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x^{x}} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + x^{x^{x^{x}}} \left(x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \frac{2 x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right)$$
Tercera derivada
[src]
/ / x /1 \\ \
| / x\ | 2 2*x *|- + (1 + log(x))*log(x)|| |
/ / / x\\\ | / x / 1 log(x) 2 2*(1 + log(x))\ 2 \ / x\ \x / | 1 x / 1 log(x) 2 2*(1 + log(x))\ 2*x /1 \ \x /| x 2 / / x\ \ |
/ / x\\ | | \x /|| | / x\ 3 | x /1 \ 3*x *|- -- + ------ + (1 + log(x)) *log(x) + --------------| 2*x /1 \ | \x / /1 x /1 \ \ 3*x *|- -- + x *|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x) + x *|- + (1 + log(x))*log(x)| *log(x) + ------------------------------| 2*x /1 x /1 \ \ / / x\\ | / x /1 \\ \x / /1 x /1 \ \| / x /1 \\ |
| \x /| | \x /| | \x / / / x\ \ / x\ | / 2 \ 3 3*x *|- + (1 + log(x))*log(x)| | 2 x x | 3*x *|- + (1 + log(x))*log(x)| | x 3 3*x *|- + x *|- + (1 + log(x))*log(x)|*log(x)| | 2 | 2 x x | \x / x | 3*x *|- + x *|- + (1 + log(x))*log(x)|*log(x)| | \x /| / / x\ \ | / x\ | 2 2*x *|- + (1 + log(x))*log(x)|| x 2 2*x *|- + x *|- + (1 + log(x))*log(x)|*log(x)|| x | 2 2*x *|- + (1 + log(x))*log(x)|| |
\x / \x / |2 2*x |1 \x / /1 x /1 \ \ | \x / |2 x |2 3 3 log(x) 3*(1 + log(x)) 3*(1 + log(x)) 3*(1 + log(x))*log(x)| 3*x /1 \ \x / \ x / \x / 2*x /1 \ / 1 log(x) 2 2*(1 + log(x))\ | 3*x /1 x /1 \ \ \x \x / / \ x \ x / / \x \x / / \x / |1 \x / /1 x /1 \ \ | | 1 \x / | 1 x / 1 log(x) 2 2*(1 + log(x))\ 2*x /1 \ \x /| 2*x /1 x /1 \ \ \x \x / /| 2*x /1 x /1 \ \ | 1 x / 1 log(x) 2 2*(1 + log(x))\ 2*x /1 \ \x /| |
x *x *|-- + x *|- + x *|- + x *|- + (1 + log(x))*log(x)|*log(x)|*log(x)| + x *|-- + x *|-- + -- + (1 + log(x)) *log(x) - ------ - -------------- + --------------- + ---------------------|*log(x) + x *|- + (1 + log(x))*log(x)| *log(x) - ------------------------------ + ------------------------------------------------------------ + --------------------------------- + 3*x *|- + (1 + log(x))*log(x)|*|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x)|*log(x) + x *|- + x *|- + (1 + log(x))*log(x)|*log(x)| *log(x) - ------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------- + 3*x *|- + x *|- + x *|- + (1 + log(x))*log(x)|*log(x)|*log(x)|*|- -- + x *|- -- + x *|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x) + x *|- + (1 + log(x))*log(x)| *log(x) + ------------------------------|*log(x) + x *|- + x *|- + (1 + log(x))*log(x)|*log(x)| *log(x) + -------------------------------------------------| + 3*x *|- + x *|- + (1 + log(x))*log(x)|*log(x)|*|- -- + x *|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x) + x *|- + (1 + log(x))*log(x)| *log(x) + ------------------------------|*log(x)|
| 3 \x \x \x / / / | 3 | 3 2 2 2 x x | \x / 2 x x \x / | 2 x x | | \x \x / / 2 x x \x \x \x / / / | 2 | 2 | 2 x x | \x / x | \x \x / / x | \x \x / / | 2 | 2 x x | \x / x | |
\x \x \x x x x / x \ x / / x \ x \ x \ x / / / \ x \ x / / /
$$x^{x^{x^{x}}} x^{x^{x^{x^{x}}}} \left(x^{3 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} \log{\left(x \right)} + 3 x^{2 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + x^{x^{x}} \left(x^{3 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} \log{\left(x \right)} + 3 x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{3} \log{\left(x \right)} + \frac{3 \left(\log{\left(x \right)} + 1\right)^{2}}{x} + \frac{3 \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)}}{x} - \frac{3 \left(\log{\left(x \right)} + 1\right)}{x^{2}} - \frac{\log{\left(x \right)}}{x^{2}} + \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) \log{\left(x \right)} + \frac{3 x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2}}{x} + \frac{3 x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right)}{x} - \frac{3 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x^{2}} + \frac{2}{x^{3}}\right) \log{\left(x \right)} + x^{2 x^{x^{x}}} \left(x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{x^{x^{x}}} \left(x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(x^{2 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x^{x}} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right) + \frac{3 x^{2 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2}}{x} + \frac{3 x^{x^{x}} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right)}{x} - \frac{3 x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x^{2}} + \frac{2}{x^{3}}\right)$$