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^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de y=-6/x
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Expresiones idénticas
- y=(ctgx^ uno / tres)^x
- y es igual a (ctgx en el grado 1 dividir por 3) en el grado x
- y es igual a (ctgx en el grado uno dividir por tres) en el grado x
- y=(ctgx1/3)x
- y=ctgx1/3x
- y=ctgx^1/3^x
- y=(ctgx^1 dividir por 3)^x
Derivada de y=(ctgx^1/3)^x
Solución
Ha introducido
[src]
x 3 ________ \/ cot(x)
$$\left(\sqrt[3]{\cot{\left(x \right)}}\right)^{x}$$
(cot(x)^(1/3))^x
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ / 2 \ \
x | | 1 cot (x)| |
- |x*|- - - -------| |
3 | \ 3 3 / /3 ________\|
(cot(x)) *|----------------- + log\\/ cot(x) /|
\ cot(x) /
$$\left(\frac{x \left(- \frac{\cot^{2}{\left(x \right)}}{3} - \frac{1}{3}\right)}{\cot{\left(x \right)}} + \log{\left(\sqrt[3]{\cot{\left(x \right)}} \right)}\right) \cot^{\frac{x}{3}}{\left(x \right)}$$
Segunda derivada
[src]
/ / / 2 \\ / / 2 \\\
x | | x*\1 + cot (x)/| | /3 ________\ x*\1 + cot (x)/||
- | / / 2 \\ |-log(cot(x)) + ---------------|*|- 3*log\\/ cot(x) / + ---------------||
3 | / 2 \ | 2 x*\1 + cot (x)/| \ cot(x) / \ cot(x) /|
(cot(x)) *|- \1 + cot (x)/*|-2*x + ------ + ---------------| + ------------------------------------------------------------------------|
| | cot(x) 2 | 3 |
\ \ cot (x) / /
----------------------------------------------------------------------------------------------------------------------------------------
3
$$\frac{\left(\frac{\left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - 3 \log{\left(\sqrt[3]{\cot{\left(x \right)}} \right)}\right) \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)}\right)}{3} - \left(\cot^{2}{\left(x \right)} + 1\right) \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot^{2}{\left(x \right)}} - 2 x + \frac{2}{\cot{\left(x \right)}}\right)\right) \cot^{\frac{x}{3}}{\left(x \right)}}{3}$$
Tercera derivada
[src]
/ 2 / / 2 \\ / / 2 \\ / / 2 \\ / / 2 \\ \
| / / 2 \\ / / 2 \\ / 2 \ | /3 ________\ x*\1 + cot (x)/| | 2 x*\1 + cot (x)/| / 2 \ | x*\1 + cot (x)/| | 2 x*\1 + cot (x)/| |
x | 2 | x*\1 + cot (x)/| | /3 ________\ x*\1 + cot (x)/| 3 \1 + cot (x)/*|- 3*log\\/ cot(x) / + ---------------|*|-2*x + ------ + ---------------| 2*\1 + cot (x)/*|-log(cot(x)) + ---------------|*|-2*x + ------ + ---------------| 2|
- | / 2 \ |-log(cot(x)) + ---------------| *|- 3*log\\/ cot(x) / + ---------------| / 2 \ / 2 \ \ cot(x) / | cot(x) 2 | \ cot(x) / | cot(x) 2 | / 2 \ |
3 | 2 \1 + cot (x)/ \ cot(x) / \ cot(x) / 4*x*\1 + cot (x)/*cot(x) 2*x*\1 + cot (x)/ \ cot (x) / \ cot (x) / 4*x*\1 + cot (x)/ |
(cot(x)) *|2 + 2*cot (x) - -------------- - ------------------------------------------------------------------------- - ------------------------ - ------------------ + --------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------- + ------------------|
| 2 27 3 3 9 9 3*cot(x) |
\ cot (x) 3*cot (x) /
$$\left(- \frac{2 x \left(\cot^{2}{\left(x \right)} + 1\right)^{3}}{3 \cot^{3}{\left(x \right)}} + \frac{4 x \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{3 \cot{\left(x \right)}} - \frac{4 x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{3} - \frac{\left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - 3 \log{\left(\sqrt[3]{\cot{\left(x \right)}} \right)}\right) \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)}\right)^{2}}{27} + \frac{\left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - 3 \log{\left(\sqrt[3]{\cot{\left(x \right)}} \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot^{2}{\left(x \right)}} - 2 x + \frac{2}{\cot{\left(x \right)}}\right)}{9} + \frac{2 \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot^{2}{\left(x \right)}} - 2 x + \frac{2}{\cot{\left(x \right)}}\right)}{9} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} + 2 \cot^{2}{\left(x \right)} + 2\right) \cot^{\frac{x}{3}}{\left(x \right)}$$
Gráfico