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/(x+3)
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Derivada de 4*y
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Derivada de (2x-7)^8
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Derivada de (-1)/x-3*x
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Expresiones idénticas
- y=(ctg(x))^sin(x)
- y es igual a (ctg(x)) en el grado seno de (x)
- y=(ctg(x))sin(x)
- y=ctgxsinx
- y=ctgx^sinx
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Expresiones semejantes
- y=(ctg(x))^sinx
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Expresiones con funciones
- Seno sin
- sin^5*x
- sin(x)^(2)*2^x^2
- sin^4(x^2-7)
- sin(x^2-7)^(4)
- sin^n(x)
Derivada de y=(ctg(x))^sin(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]
/ / 2 \ \
sin(x) | \-1 - cot (x)/*sin(x)|
cot (x)*|cos(x)*log(cot(x)) + ---------------------|
\ cot(x) /
$$\left(\frac{\left(- \cot^{2}{\left(x \right)} - 1\right) \sin{\left(x \right)}}{\cot{\left(x \right)}} + \log{\left(\cot{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cot^{\sin{\left(x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
sin(x) || \1 + cot (x)/*sin(x)| / 2 \ \1 + cot (x)/ *sin(x) 2*\1 + cot (x)/*cos(x)|
cot (x)*||-cos(x)*log(cot(x)) + --------------------| - log(cot(x))*sin(x) + 2*\1 + cot (x)/*sin(x) - --------------------- - ----------------------|
|\ cot(x) / 2 cot(x) |
\ cot (x) /
$$\left(\left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)} \cos{\left(x \right)}\right)^{2} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\cot^{2}{\left(x \right)}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)} \sin{\left(x \right)}\right) \cot^{\sin{\left(x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 2 3 2 \
| / / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
sin(x) | | \1 + cot (x)/*sin(x)| | \1 + cot (x)/*sin(x)| | / 2 \ \1 + cot (x)/ *sin(x) 2*\1 + cot (x)/*cos(x)| / 2 \ / 2 \ 3*\1 + cot (x)/ *cos(x) 2*\1 + cot (x)/ *sin(x) 3*\1 + cot (x)/*sin(x) 4*\1 + cot (x)/ *sin(x)|
cot (x)*|- |-cos(x)*log(cot(x)) + --------------------| - cos(x)*log(cot(x)) + 3*|-cos(x)*log(cot(x)) + --------------------|*|log(cot(x))*sin(x) - 2*\1 + cot (x)/*sin(x) + --------------------- + ----------------------| + 6*\1 + cot (x)/*cos(x) - 4*\1 + cot (x)/*cot(x)*sin(x) - ----------------------- - ----------------------- + ---------------------- + -----------------------|
| \ cot(x) / \ cot(x) / | 2 cot(x) | 2 3 cot(x) cot(x) |
\ \ cot (x) / cot (x) cot (x) /
$$\left(- \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)} \cos{\left(x \right)}\right)^{3} + 3 \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)} \cos{\left(x \right)}\right) \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\cot^{2}{\left(x \right)}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cot{\left(x \right)}} + \log{\left(\cot{\left(x \right)} \right)} \sin{\left(x \right)}\right) - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \sin{\left(x \right)}}{\cot^{3}{\left(x \right)}} + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\cot{\left(x \right)}} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\cot^{2}{\left(x \right)}} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} \cot{\left(x \right)} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cot{\left(x \right)}} + 6 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} - \log{\left(\cot{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cot^{\sin{\left(x \right)}}{\left(x \right)}$$
Gráfico