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 6/x
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Derivada de e^(x/2)
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Derivada de (x-1)/(x+1)
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Derivada de -3/x
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Expresiones idénticas
- y=(ctgx)^cosx
- y es igual a (ctgx) en el grado coseno de x
- y=(ctgx)cosx
- y=ctgxcosx
- y=ctgx^cosx
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Expresiones con funciones
- cosx
- cosx/1+sinx
- cosx/e^x
- cosx^1/2
- cosx^(sinx)
- cosx/√(x^2-1)
Derivada de y=(ctgx)^cosx
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 \ \
cos(x) | \-1 - cot (x)/*cos(x)|
cot (x)*|-log(cot(x))*sin(x) + ---------------------|
\ cot(x) /
$$\left(\frac{\left(- \cot^{2}{\left(x \right)} - 1\right) \cos{\left(x \right)}}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)} \sin{\left(x \right)}\right) \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
cos(x) || \1 + cot (x)/*cos(x)| / 2 \ \1 + cot (x)/ *cos(x) 2*\1 + cot (x)/*sin(x)|
cot (x)*||log(cot(x))*sin(x) + --------------------| - cos(x)*log(cot(x)) + 2*\1 + cot (x)/*cos(x) - --------------------- + ----------------------|
|\ cot(x) / 2 cot(x) |
\ cot (x) /
$$\left(\left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cot{\left(x \right)}} + \log{\left(\cot{\left(x \right)} \right)} \sin{\left(x \right)}\right)^{2} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\cot^{2}{\left(x \right)}} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cot{\left(x \right)}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} - \log{\left(\cot{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 3 2 2 \
| / / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
cos(x) | | \1 + cot (x)/*cos(x)| / 2 \ | \1 + cot (x)/*cos(x)| | / 2 \ \1 + cot (x)/ *cos(x) 2*\1 + cot (x)/*sin(x)| / 2 \ 2*\1 + cot (x)/ *cos(x) 3*\1 + cot (x)/ *sin(x) 3*\1 + cot (x)/*cos(x) 4*\1 + cot (x)/ *cos(x)|
cot (x)*|- |log(cot(x))*sin(x) + --------------------| + log(cot(x))*sin(x) - 6*\1 + cot (x)/*sin(x) + 3*|log(cot(x))*sin(x) + --------------------|*|cos(x)*log(cot(x)) - 2*\1 + cot (x)/*cos(x) + --------------------- - ----------------------| - 4*\1 + cot (x)/*cos(x)*cot(x) - ----------------------- + ----------------------- + ---------------------- + -----------------------|
| \ cot(x) / \ cot(x) / | 2 cot(x) | 3 2 cot(x) cot(x) |
\ \ cot (x) / cot (x) cot (x) /
$$\left(- \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cot{\left(x \right)}} + \log{\left(\cot{\left(x \right)} \right)} \sin{\left(x \right)}\right)^{3} + 3 \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cot{\left(x \right)}} + \log{\left(\cot{\left(x \right)} \right)} \sin{\left(x \right)}\right) \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\cot^{2}{\left(x \right)}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cot{\left(x \right)}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} + \log{\left(\cot{\left(x \right)} \right)} \cos{\left(x \right)}\right) - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \cos{\left(x \right)}}{\cot^{3}{\left(x \right)}} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\cot^{2}{\left(x \right)}} + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\cot{\left(x \right)}} - 6 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} \cot{\left(x \right)} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cot{\left(x \right)}} + \log{\left(\cot{\left(x \right)} \right)} \sin{\left(x \right)}\right) \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
Gráfico