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 x^-(4/5)
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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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Expresiones idénticas
- (x+sin(x-e))^lne^x
- (x más seno de (x menos e)) en el grado lne en el grado x
- (x+sin(x-e))lnex
- x+sinx-elnex
- x+sinx-e^lne^x
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Expresiones semejantes
- (x-sin(x-e))^lne^x
- (x+sin(x+e))^lne^x
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Expresiones con funciones
- Seno sin
- sin*x^2
- sin(x)^(6)
- sin(x)^(5*x)
- sin(x+2)
- sin(x^3-x)/(x^3-x)+sin(x^3-x)
Derivada de (x+sin(x-e))^lne^x
Solución
Ha introducido
[src]
x
log (E)
(x + sin(x - E))
$$\left(x + \sin{\left(x - e \right)}\right)^{\log{\left(e \right)}^{x}}$$
(x + sin(x - E))^(log(E)^x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
x / x \
log (E) |log (E)*(1 + cos(x - E)) x |
(x + sin(x - E)) *|------------------------ + log (E)*log(x + sin(x - E))*log(log(E))|
\ x + sin(x - E) /
$$\left(x + \sin{\left(x - e \right)}\right)^{\log{\left(e \right)}^{x}} \left(\log{\left(e \right)}^{x} \log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)} + \frac{\left(\cos{\left(x - e \right)} + 1\right) \log{\left(e \right)}^{x}}{x + \sin{\left(x - e \right)}}\right)$$
Segunda derivada
[src]
x / 2 2 \
log (E) x |/1 + cos(x - E) \ x 2 (1 + cos(x - E)) sin(x - E) 2*(1 + cos(x - E))*log(log(E))|
(x + sin(x - E)) *log (E)*||-------------- + log(x + sin(x - E))*log(log(E))| *log (E) + log (log(E))*log(x + sin(x - E)) - ----------------- - -------------- + ------------------------------|
|\x + sin(x - E) / 2 x + sin(x - E) x + sin(x - E) |
\ (x + sin(x - E)) /
$$\left(x + \sin{\left(x - e \right)}\right)^{\log{\left(e \right)}^{x}} \left(\left(\log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)} + \frac{\cos{\left(x - e \right)} + 1}{x + \sin{\left(x - e \right)}}\right)^{2} \log{\left(e \right)}^{x} + \log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)}^{2} + \frac{2 \left(\cos{\left(x - e \right)} + 1\right) \log{\left(\log{\left(e \right)} \right)}}{x + \sin{\left(x - e \right)}} - \frac{\sin{\left(x - e \right)}}{x + \sin{\left(x - e \right)}} - \frac{\left(\cos{\left(x - e \right)} + 1\right)^{2}}{\left(x + \sin{\left(x - e \right)}\right)^{2}}\right) \log{\left(e \right)}^{x}$$
Tercera derivada
[src]
x / 3 3 2 2 / 2 \\
log (E) x |/1 + cos(x - E) \ 2*x 3 cos(x - E) 2*(1 + cos(x - E)) 3*(1 + cos(x - E)) *log(log(E)) 3*log(log(E))*sin(x - E) 3*log (log(E))*(1 + cos(x - E)) 3*(1 + cos(x - E))*sin(x - E) x /1 + cos(x - E) \ | 2 (1 + cos(x - E)) sin(x - E) 2*(1 + cos(x - E))*log(log(E))||
(x + sin(x - E)) *log (E)*||-------------- + log(x + sin(x - E))*log(log(E))| *log (E) + log (log(E))*log(x + sin(x - E)) - -------------- + ------------------- - ------------------------------- - ------------------------ + ------------------------------- + ----------------------------- + 3*log (E)*|-------------- + log(x + sin(x - E))*log(log(E))|*|log (log(E))*log(x + sin(x - E)) - ----------------- - -------------- + ------------------------------||
|\x + sin(x - E) / x + sin(x - E) 3 2 x + sin(x - E) x + sin(x - E) 2 \x + sin(x - E) / | 2 x + sin(x - E) x + sin(x - E) ||
\ (x + sin(x - E)) (x + sin(x - E)) (x + sin(x - E)) \ (x + sin(x - E)) //
$$\left(x + \sin{\left(x - e \right)}\right)^{\log{\left(e \right)}^{x}} \left(\left(\log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)} + \frac{\cos{\left(x - e \right)} + 1}{x + \sin{\left(x - e \right)}}\right)^{3} \log{\left(e \right)}^{2 x} + 3 \left(\log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)} + \frac{\cos{\left(x - e \right)} + 1}{x + \sin{\left(x - e \right)}}\right) \left(\log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)}^{2} + \frac{2 \left(\cos{\left(x - e \right)} + 1\right) \log{\left(\log{\left(e \right)} \right)}}{x + \sin{\left(x - e \right)}} - \frac{\sin{\left(x - e \right)}}{x + \sin{\left(x - e \right)}} - \frac{\left(\cos{\left(x - e \right)} + 1\right)^{2}}{\left(x + \sin{\left(x - e \right)}\right)^{2}}\right) \log{\left(e \right)}^{x} + \log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)}^{3} + \frac{3 \left(\cos{\left(x - e \right)} + 1\right) \log{\left(\log{\left(e \right)} \right)}^{2}}{x + \sin{\left(x - e \right)}} - \frac{3 \log{\left(\log{\left(e \right)} \right)} \sin{\left(x - e \right)}}{x + \sin{\left(x - e \right)}} - \frac{\cos{\left(x - e \right)}}{x + \sin{\left(x - e \right)}} - \frac{3 \left(\cos{\left(x - e \right)} + 1\right)^{2} \log{\left(\log{\left(e \right)} \right)}}{\left(x + \sin{\left(x - e \right)}\right)^{2}} + \frac{3 \left(\cos{\left(x - e \right)} + 1\right) \sin{\left(x - e \right)}}{\left(x + \sin{\left(x - e \right)}\right)^{2}} + \frac{2 \left(\cos{\left(x - e \right)} + 1\right)^{3}}{\left(x + \sin{\left(x - e \right)}\right)^{3}}\right) \log{\left(e \right)}^{x}$$
Gráfico