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Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
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- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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- Derivada de:
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Derivada de (t^(2)+1)÷(t^(1÷2)-1)
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Expresiones idénticas
- x^(x^x^x)
- x en el grado (x en el grado x en el grado x)
- x(xxx)
- xxxx
- x^x^x^x
Derivada de x^(x^x^x)
Solución
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ / x\\ / / x\ \
| \x /| | \x / / x\ / x \ |
\x / |x \x / |x x | |
x *|----- + x *|-- + x *(1 + log(x))*log(x)|*log(x)|
\ x \x / /
$$x^{x^{x^{x}}} \left(x^{x^{x}} \left(x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{x^{x}}{x}\right) \log{\left(x \right)} + \frac{x^{x^{x}}}{x}\right)$$
Segunda derivada
[src]
/ / x\\ / x /1 \\
/ x\ | \x /| | / x\ 2 2 2*x *|- + (1 + log(x))*log(x)||
\x / \x / | 1 \x / /1 x /1 \ \ x / 1 log(x) 2 2*(1 + log(x))\ 2*x /1 \ \x /|
x *x *|- -- + 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) + ------------------------------|
| 2 \x \x / / | 2 x x | \x / x |
\ x \ x / /
$$x^{x^{x}} x^{x^{x^{x}}} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right)$$
Tercera derivada
[src]
/ x / 1 log(x) 2 2*(1 + log(x))\ 2 \
/ / x\\ | x /1 \ 3*x *|- -- + ------ + (1 + log(x)) *log(x) + --------------| 2*x /1 \ / x /1 \\ |
/ x\ | \x /| | x 3 / 2 \ 3 3*x *|- + (1 + log(x))*log(x)| | 2 x x | 3*x *|- + (1 + log(x))*log(x)| / x\ | 2 2*x *|- + (1 + log(x))*log(x)|| |
\x / \x / |2 2*x /1 x /1 \ \ 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 / \x / /1 x /1 \ \ | 1 x / 1 log(x) 2 2*(1 + log(x))\ 2*x /1 \ \x /| 2*x /1 \ / 1 log(x) 2 2*(1 + log(x))\ |
x *x *|-- + 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) - ------------------------------ + ------------------------------------------------------------ + --------------------------------- + 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) + ------------------------------| + 3*x *|- + (1 + log(x))*log(x)|*|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x)|
| 3 \x \x / / | 3 2 2 2 x x | \x / 2 x x \x \x / / | 2 | 2 x x | \x / x | \x / | 2 x x | |
\x \x x x x / x \ x \ x / / \ x / /
$$x^{x^{x}} x^{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)} + 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)^{3} + 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) \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) + \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)$$
3-я производная
[src]
/ x / 1 log(x) 2 2*(1 + log(x))\ 2 \
/ / x\\ | x /1 \ 3*x *|- -- + ------ + (1 + log(x)) *log(x) + --------------| 2*x /1 \ / x /1 \\ |
/ x\ | \x /| | x 3 / 2 \ 3 3*x *|- + (1 + log(x))*log(x)| | 2 x x | 3*x *|- + (1 + log(x))*log(x)| / x\ | 2 2*x *|- + (1 + log(x))*log(x)|| |
\x / \x / |2 2*x /1 x /1 \ \ 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 / \x / /1 x /1 \ \ | 1 x / 1 log(x) 2 2*(1 + log(x))\ 2*x /1 \ \x /| 2*x /1 \ / 1 log(x) 2 2*(1 + log(x))\ |
x *x *|-- + 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) - ------------------------------ + ------------------------------------------------------------ + --------------------------------- + 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) + ------------------------------| + 3*x *|- + (1 + log(x))*log(x)|*|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x)|
| 3 \x \x / / | 3 2 2 2 x x | \x / 2 x x \x \x / / | 2 | 2 x x | \x / x | \x / | 2 x x | |
\x \x x x x / x \ x \ x / / \ x / /
$$x^{x^{x}} x^{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)} + 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)^{3} + 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) \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) + \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)$$