Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
-
¿Cómo usar?
- Derivada de:
-
Derivada de 2*cos(3*x)
-
Derivada de x^(7/6)
-
Derivada de x^(2/5)
-
Derivada de 1/ln(x)
-
Expresiones idénticas
- x^(x^(x))lnx*x^(x)lnx
- x en el grado (x en el grado (x))lnx multiplicar por x en el grado (x)lnx
- x(x(x))lnx*x(x)lnx
- xxxlnx*xxlnx
- x^(x^(x))lnxx^(x)lnx
- x(x(x))lnxx(x)lnx
- xxxlnxxxlnx
- x^x^xlnxx^xlnx
Derivada de x^(x^(x))lnx*x^(x)lnx
Solución
Ha introducido
[src]
/ x\ \x / x x *log(x)*x *log(x)
$$x^{x} x^{x^{x}} \log{\left(x \right)} \log{\left(x \right)}$$
((x^(x^x)*log(x))*x^x)*log(x)
Solución detallada
-
Se aplica la regla de la derivada de una multiplicación:
; calculamos :
-
Se aplica la regla de la derivada de una multiplicación:
; calculamos :
-
Se aplica la regla de la derivada de una multiplicación:
; calculamos :
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
; calculamos :
-
Derivado es .
Como resultado de:
-
; calculamos :
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de:
-
; calculamos :
-
Derivado es .
Como resultado de:
-
-
Simplificamos:
Respuesta:
Primera derivada
[src]
/ / / x\ \ \ / x\ | | \x / / x\ / x \ | / x\ | x \x / | x |x \x / |x x | | x \x / | x *x *log(x) |x *|----- + x *|-- + x *(1 + log(x))*log(x)|*log(x)| + x *x *(1 + log(x))*log(x)|*log(x) + --------------- \ \ x \x / / / x
$$\left(x^{x} x^{x^{x}} \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + x^{x} \left(x^{x^{x}} \left(x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{x^{x}}{x}\right) \log{\left(x \right)} + \frac{x^{x^{x}}}{x}\right)\right) \log{\left(x \right)} + \frac{x^{x} x^{x^{x}} \log{\left(x \right)}}{x}$$
Segunda derivada
[src]
// x /1 \\ /1 x /1 \ \\
/ x\ || / 2 \ 2*x *|- + (1 + log(x))*log(x)|| 2*|- + (1 + log(x))*log(x) + x *|- + (1 + log(x))*log(x)|*log(x)||
x \x / || 1 /1 2\ /1 x /1 \ \ x | 1 log(x) x /1 \ 2 2*(1 + log(x))| \x /| log(x) \x \x / /|
x *x *||- -- + |- + (1 + log(x)) |*log(x) + 2*(1 + log(x))*|- + x *|- + (1 + log(x))*log(x)|*log(x)| + x *|- -- + ------ + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) + --------------|*log(x) + ------------------------------|*log(x) - ------ + -----------------------------------------------------------------|
|| 2 \x / \x \x / / | 2 x \x / x | x | 2 x |
\\ x \ x / / x /
$$x^{x} x^{x^{x}} \left(\left(x^{x} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + 2 \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} + 1\right) + \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{\log{\left(x \right)}}{x^{2}}\right)$$
Tercera derivada
[src]
/ / x /1 \\\
|/ / 2 \\ | / 2 \ 2*x *|- + (1 + log(x))*log(x)|||
|| x | 1 log(x) x /1 \ 2 2*(1 + log(x))|| | 1 /1 2\ /1 x /1 \ \ x | 1 log(x) x /1 \ 2 2*(1 + log(x))| \x /||
|| / x /1 \\ x /1 \ 3*x *|- -- + ------ + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) + --------------|| /1 x /1 \ \ 3*|- -- + |- + (1 + log(x)) |*log(x) + 2*(1 + log(x))*|- + x *|- + (1 + log(x))*log(x)|*log(x)| + x *|- -- + ------ + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) + --------------|*log(x) + ------------------------------||
/ x\ || | / 2 \ 2*x *|- + (1 + log(x))*log(x)|| / 3 2 \ 3*x *|- + (1 + log(x))*log(x)| | 2 x \x / x || 3*|- + (1 + log(x))*log(x) + x *|- + (1 + log(x))*log(x)|*log(x)| | 2 \x / \x \x / / | 2 x \x / x | x ||
x \x / ||2 / 3 1 3*(1 + log(x))\ | 1 x | 1 log(x) x /1 \ 2 2*(1 + log(x))| \x /| /1 2\ /1 x /1 \ \ x |2 3 2*x /1 \ 3 log(x) 3*(1 + log(x)) 3*(1 + log(x)) 3*(1 + log(x))*log(x) x /1 \ / 1 log(x) 2 2*(1 + log(x))\| \x / \ x /| \x \x / / 2*log(x) \ x \ x / /|
x *x *||-- + |(1 + log(x)) - -- + --------------|*log(x) + 3*(1 + log(x))*|- -- + x *|- -- + ------ + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) + --------------|*log(x) + ------------------------------| + 3*|- + (1 + log(x)) |*|- + x *|- + (1 + log(x))*log(x)|*log(x)| + x *|-- + -- + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) - ------ - -------------- + --------------- + --------------------- + 3*x *|- + (1 + log(x))*log(x)|*|- -- + ------ + (1 + log(x)) *log(x) + --------------||*log(x) - ------------------------------ + --------------------------------------------------------------------------------------------|*log(x) - ----------------------------------------------------------------- + -------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
|| 3 | 2 x | | 2 | 2 x \x / x | x | \x / \x \x / / | 3 2 \x / 2 2 x x \x / | 2 x x || 2 x | 2 3 x |
\\x \ x / \ x \ x / / \x x x x \ x // x / x x /
$$x^{x} x^{x^{x}} \left(\left(x^{x} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{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) + \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)} + 3 \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(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) + 3 \left(\log{\left(x \right)} + 1\right) \left(x^{x} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \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) + \left(\left(\log{\left(x \right)} + 1\right)^{3} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{3 x^{x} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \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)} + \frac{3 \left(x^{x} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \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)} + 2 \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(\log{\left(x \right)} + 1\right) + \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\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 \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x^{2}} + \frac{2 \log{\left(x \right)}}{x^{3}}\right)$$