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
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¿Cómo usar?
- Derivada de:
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Derivada de (sqrt(x)-1)/sqrt(x^2-x-1)
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Derivada de 1/x^5
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Derivada de 7*x
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Derivada de √x
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Expresiones idénticas
- x^(x^ tres +ln(x)^x)
- x en el grado (x al cubo más ln(x) en el grado x)
- x en el grado (x en el grado tres más ln(x) en el grado x)
- x(x3+ln(x)x)
- xx3+lnxx
- x^(x³+ln(x)^x)
- x en el grado (x en el grado 3+ln(x) en el grado x)
- x^x^3+lnx^x
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Expresiones semejantes
- x^(x^3-ln(x)^x)
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Expresiones con funciones
- ln
- ln(1+2x)
- ln((1+x)/(1-x))
- ln(x)+x
- ln(x+4)^11
- ln(2x)/x
Derivada de x^(x^3+ln(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]
3 x / 3 x \
x + log (x) |x + log (x) / 2 x / 1 \\ |
x *|------------ + |3*x + log (x)*|------ + log(log(x))||*log(x)|
\ x \ \log(x) // /
$$x^{x^{3} + \log{\left(x \right)}^{x}} \left(\left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right) \log{\left(x \right)} + \frac{x^{3} + \log{\left(x \right)}^{x}}{x}\right)$$
Segunda derivada
[src]
/ 2 / x / 1 \\ / 2 x / 1 \\\
3 x |/ 3 x \ | 2 log (x)*|1 - ------|| 3 x 2*|3*x + log (x)*|------ + log(log(x))|||
x + log (x) ||x + log (x) / 2 x / 1 \\ | | / 1 \ x \ log(x)/| x + log (x) \ \log(x) //|
x *||------------ + |3*x + log (x)*|------ + log(log(x))||*log(x)| + |6*x + |------ + log(log(x))| *log (x) + --------------------|*log(x) - ------------ + -----------------------------------------|
|\ x \ \log(x) // / \ \log(x) / x*log(x) / 2 x |
\ x /
$$x^{x^{3} + \log{\left(x \right)}^{x}} \left(\left(\left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right) \log{\left(x \right)} + \frac{x^{3} + \log{\left(x \right)}^{x}}{x}\right)^{2} + \left(6 x + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} \log{\left(x \right)}^{x} + \frac{\left(1 - \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}}\right) \log{\left(x \right)} + \frac{2 \left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right)}{x} - \frac{x^{3} + \log{\left(x \right)}^{x}}{x^{2}}\right)$$
Tercera derivada
[src]
/ / x / 1 \\ \
| / x / 2 \ \ | 2 log (x)*|1 - ------|| |
| 3 | log (x)*|1 - -------| x / 1 \ / 1 \| / 2 x / 1 \\ | / 1 \ x \ log(x)/| // x / 1 \\ / 2 x / 1 \\\|
3 x |/ 3 x \ | 3 | 2 | 3*log (x)*|1 - ------|*|------ + log(log(x))|| 3*|3*x + log (x)*|------ + log(log(x))|| / 3 x \ 3*|6*x + |------ + log(log(x))| *log (x) + --------------------| / 3 x \ || 2 log (x)*|1 - ------|| 3 x 2*|3*x + log (x)*|------ + log(log(x))||||
x + log (x) ||x + log (x) / 2 x / 1 \\ | | / 1 \ x \ log (x)/ \ log(x)/ \log(x) /| \ \log(x) // 2*\x + log (x)/ \ \log(x) / x*log(x) / |x + log (x) / 2 x / 1 \\ | || / 1 \ x \ log(x)/| x + log (x) \ \log(x) //||
x *||------------ + |3*x + log (x)*|------ + log(log(x))||*log(x)| + |6 + |------ + log(log(x))| *log (x) - --------------------- + ---------------------------------------------|*log(x) - ----------------------------------------- + ---------------- + ---------------------------------------------------------------- + 3*|------------ + |3*x + log (x)*|------ + log(log(x))||*log(x)|*||6*x + |------ + log(log(x))| *log (x) + --------------------|*log(x) - ------------ + -----------------------------------------||
|\ x \ \log(x) // / | \log(x) / 2 x*log(x) | 2 3 x \ x \ \log(x) // / |\ \log(x) / x*log(x) / 2 x ||
\ \ x *log(x) / x x \ x //
$$x^{x^{3} + \log{\left(x \right)}^{x}} \left(\left(\left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right) \log{\left(x \right)} + \frac{x^{3} + \log{\left(x \right)}^{x}}{x}\right)^{3} + 3 \left(\left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right) \log{\left(x \right)} + \frac{x^{3} + \log{\left(x \right)}^{x}}{x}\right) \left(\left(6 x + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} \log{\left(x \right)}^{x} + \frac{\left(1 - \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}}\right) \log{\left(x \right)} + \frac{2 \left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right)}{x} - \frac{x^{3} + \log{\left(x \right)}^{x}}{x^{2}}\right) + \left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} \log{\left(x \right)}^{x} + 6 + \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}} - \frac{\left(1 - \frac{2}{\log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{x}}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)} + \frac{3 \left(6 x + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} \log{\left(x \right)}^{x} + \frac{\left(1 - \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}}\right)}{x} - \frac{3 \left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right)}{x^{2}} + \frac{2 \left(x^{3} + \log{\left(x \right)}^{x}\right)}{x^{3}}\right)$$