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:
- Derivada de e^((3*x)^2)
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Derivada de d/dx(x)
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Derivada de (cos(x))^x^2
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Derivada de (8*x-15)^5
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Expresiones idénticas
- (x^ln2x)/(ln2x)^x
- (x en el grado ln2x) dividir por (ln2x) en el grado x
- (xln2x)/(ln2x)x
- xln2x/ln2xx
- x^ln2x/ln2x^x
- (x^ln2x) dividir por (ln2x)^x
Derivada de (x^ln2x)/(ln2x)^x
Solución
Ha introducido
[src]
log(2*x) x --------- x log (2*x)
$$\frac{x^{\log{\left(2 x \right)}}}{\log{\left(2 x \right)}^{x}}$$
x^log(2*x)/log(2*x)^x
Solución detallada
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Se aplica la regla de la derivada parcial:
y .
Para calcular :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Para calcular :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Ahora aplicamos la regla de la derivada de una divesión:
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Simplificamos:
Respuesta:
Primera derivada
[src]
log(2*x) -x / 1 \ log(2*x) -x /log(x) log(2*x)\
x *log (2*x)*|- -------- - log(log(2*x))| + x *log (2*x)*|------ + --------|
\ log(2*x) / \ x x /
$$x^{\log{\left(2 x \right)}} \left(\frac{\log{\left(x \right)}}{x} + \frac{\log{\left(2 x \right)}}{x}\right) \log{\left(2 x \right)}^{- x} + x^{\log{\left(2 x \right)}} \left(- \log{\left(\log{\left(2 x \right)} \right)} - \frac{1}{\log{\left(2 x \right)}}\right) \log{\left(2 x \right)}^{- x}$$
Segunda derivada
[src]
/ 1 / 1 \ \
| 2 2 1 - -------- 2*|-------- + log(log(2*x))|*(log(x) + log(2*x))|
log(2*x) -x |/ 1 \ 2 + (log(x) + log(2*x)) - log(x) - log(2*x) log(2*x) \log(2*x) / |
x *log (2*x)*||-------- + log(log(2*x))| + -------------------------------------------- - ------------ - ------------------------------------------------|
|\log(2*x) / 2 x*log(2*x) x |
\ x /
$$x^{\log{\left(2 x \right)}} \left(\left(\log{\left(\log{\left(2 x \right)} \right)} + \frac{1}{\log{\left(2 x \right)}}\right)^{2} - \frac{1 - \frac{1}{\log{\left(2 x \right)}}}{x \log{\left(2 x \right)}} - \frac{2 \left(\log{\left(x \right)} + \log{\left(2 x \right)}\right) \left(\log{\left(\log{\left(2 x \right)} \right)} + \frac{1}{\log{\left(2 x \right)}}\right)}{x} + \frac{\left(\log{\left(x \right)} + \log{\left(2 x \right)}\right)^{2} - \log{\left(x \right)} - \log{\left(2 x \right)} + 2}{x^{2}}\right) \log{\left(2 x \right)}^{- x}$$
Tercera derivada
[src]
/ / 1 \ \
| 2 | 2 1 - --------| |
| 1 - --------- / 1 \ / 2 \ |/ 1 \ log(2*x)| / 1 \ / 1 \|
| 3 3 2 3*|-------- + log(log(2*x))|*\2 + (log(x) + log(2*x)) - log(x) - log(2*x)/ 3*||-------- + log(log(2*x))| - ------------|*(log(x) + log(2*x)) 3*|1 - --------|*|-------- + log(log(2*x))||
log(2*x) -x | / 1 \ -6 + (log(x) + log(2*x)) + 2*log(x) + 2*log(2*x) - 3*(log(x) + log(2*x))*(-2 + log(x) + log(2*x)) log (2*x) \log(2*x) / \\log(2*x) / x*log(2*x) / \ log(2*x)/ \log(2*x) /|
x *log (2*x)*|- |-------- + log(log(2*x))| + -------------------------------------------------------------------------------------------------- + ------------- - --------------------------------------------------------------------------- + ------------------------------------------------------------------ + -------------------------------------------|
| \log(2*x) / 3 2 2 x x*log(2*x) |
\ x x *log(2*x) x /
$$x^{\log{\left(2 x \right)}} \left(- \left(\log{\left(\log{\left(2 x \right)} \right)} + \frac{1}{\log{\left(2 x \right)}}\right)^{3} + \frac{3 \left(1 - \frac{1}{\log{\left(2 x \right)}}\right) \left(\log{\left(\log{\left(2 x \right)} \right)} + \frac{1}{\log{\left(2 x \right)}}\right)}{x \log{\left(2 x \right)}} + \frac{3 \left(\left(\log{\left(\log{\left(2 x \right)} \right)} + \frac{1}{\log{\left(2 x \right)}}\right)^{2} - \frac{1 - \frac{1}{\log{\left(2 x \right)}}}{x \log{\left(2 x \right)}}\right) \left(\log{\left(x \right)} + \log{\left(2 x \right)}\right)}{x} + \frac{1 - \frac{2}{\log{\left(2 x \right)}^{2}}}{x^{2} \log{\left(2 x \right)}} - \frac{3 \left(\log{\left(\log{\left(2 x \right)} \right)} + \frac{1}{\log{\left(2 x \right)}}\right) \left(\left(\log{\left(x \right)} + \log{\left(2 x \right)}\right)^{2} - \log{\left(x \right)} - \log{\left(2 x \right)} + 2\right)}{x^{2}} + \frac{\left(\log{\left(x \right)} + \log{\left(2 x \right)}\right)^{3} - 3 \left(\log{\left(x \right)} + \log{\left(2 x \right)}\right) \left(\log{\left(x \right)} + \log{\left(2 x \right)} - 2\right) + 2 \log{\left(x \right)} + 2 \log{\left(2 x \right)} - 6}{x^{3}}\right) \log{\left(2 x \right)}^{- x}$$
Gráfico