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 1/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- y=(uno +cosx)^(ln^(dos)x)
- y es igual a (1 más coseno de x) en el grado (ln en el grado (2)x)
- y es igual a (uno más coseno de x) en el grado (ln en el grado (dos)x)
- y=(1+cosx)(ln(2)x)
- y=1+cosxln2x
- y=1+cosx^ln^2x
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Expresiones semejantes
- y=(1-cosx)^(ln^(2)x)
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Expresiones con funciones
- ln
- ln^2(2x-1)
- ln*(x+sqrt*(x^2+1))
- ln(√x)
- ln(x+1)/x^2
- ln(x^1/2)
Derivada de y=(1+cosx)^(ln^(2)x)
Solución
Ha introducido
[src]
2
log (x)
(1 + cos(x))
$$\left(\cos{\left(x \right)} + 1\right)^{\log{\left(x \right)}^{2}}$$
(1 + cos(x))^(log(x)^2)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
2 / 2 \
log (x) | log (x)*sin(x) 2*log(x)*log(1 + cos(x))|
(1 + cos(x)) *|- -------------- + ------------------------|
\ 1 + cos(x) x /
$$\left(- \frac{\log{\left(x \right)}^{2} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{2 \log{\left(x \right)} \log{\left(\cos{\left(x \right)} + 1 \right)}}{x}\right) \left(\cos{\left(x \right)} + 1\right)^{\log{\left(x \right)}^{2}}$$
Segunda derivada
[src]
2 / 2 2 2 2 \
log (x) |/ 2*log(1 + cos(x)) log(x)*sin(x)\ 2 2*log(1 + cos(x)) log (x)*cos(x) log (x)*sin (x) 2*log(x)*log(1 + cos(x)) 4*log(x)*sin(x)|
(1 + cos(x)) *||- ----------------- + -------------| *log (x) + ----------------- - -------------- - --------------- - ------------------------ - ---------------|
|\ x 1 + cos(x) / 2 1 + cos(x) 2 2 x*(1 + cos(x))|
\ x (1 + cos(x)) x /
$$\left(\cos{\left(x \right)} + 1\right)^{\log{\left(x \right)}^{2}} \left(\left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x}\right)^{2} \log{\left(x \right)}^{2} - \frac{\log{\left(x \right)}^{2} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{\log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} - \frac{4 \log{\left(x \right)} \sin{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)} - \frac{2 \log{\left(x \right)} \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{2}} + \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{2}}\right)$$
Tercera derivada
[src]
2 / 3 2 2 3 / 2 2 2 \ 2 2 \
log (x) | / 2*log(1 + cos(x)) log(x)*sin(x)\ 3 6*log(1 + cos(x)) log (x)*sin(x) 6*sin(x) 2*log (x)*sin (x) / 2*log(1 + cos(x)) log(x)*sin(x)\ | 2*log(1 + cos(x)) log (x)*cos(x) log (x)*sin (x) 2*log(x)*log(1 + cos(x)) 4*log(x)*sin(x)| 4*log(x)*log(1 + cos(x)) 6*cos(x)*log(x) 6*sin (x)*log(x) 3*log (x)*cos(x)*sin(x) 6*log(x)*sin(x)|
(1 + cos(x)) *|- |- ----------------- + -------------| *log (x) - ----------------- + -------------- - --------------- - ----------------- + 3*|- ----------------- + -------------|*|- ----------------- + -------------- + --------------- + ------------------------ + ---------------|*log(x) + ------------------------ - --------------- - ---------------- - ----------------------- + ---------------|
| \ x 1 + cos(x) / 3 1 + cos(x) 2 3 \ x 1 + cos(x) / | 2 1 + cos(x) 2 2 x*(1 + cos(x))| 3 x*(1 + cos(x)) 2 2 2 |
\ x x *(1 + cos(x)) (1 + cos(x)) \ x (1 + cos(x)) x / x x*(1 + cos(x)) (1 + cos(x)) x *(1 + cos(x))/
$$\left(\cos{\left(x \right)} + 1\right)^{\log{\left(x \right)}^{2}} \left(- \left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x}\right)^{3} \log{\left(x \right)}^{3} + 3 \left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x}\right) \left(\frac{\log{\left(x \right)}^{2} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{\log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} + \frac{4 \log{\left(x \right)} \sin{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)} + \frac{2 \log{\left(x \right)} \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{2}} - \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{2}}\right) \log{\left(x \right)} + \frac{\log{\left(x \right)}^{2} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{3 \log{\left(x \right)}^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} - \frac{2 \log{\left(x \right)}^{2} \sin^{3}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{3}} - \frac{6 \log{\left(x \right)} \cos{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)} - \frac{6 \log{\left(x \right)} \sin^{2}{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)^{2}} + \frac{6 \log{\left(x \right)} \sin{\left(x \right)}}{x^{2} \left(\cos{\left(x \right)} + 1\right)} - \frac{6 \sin{\left(x \right)}}{x^{2} \left(\cos{\left(x \right)} + 1\right)} + \frac{4 \log{\left(x \right)} \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{3}} - \frac{6 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{3}}\right)$$
Gráfico