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 e^x*sin(x)
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Derivada de x*e^(1/x)
- Derivada de x!
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Derivada de e^y
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Expresiones idénticas
- y=(ctg3x)^(2e)^x
- y es igual a (ctg3x) en el grado (2e) en el grado x
- y=(ctg3x)(2e)x
- y=ctg3x2ex
- y=ctg3x^2e^x
Derivada de y=(ctg3x)^(2e)^x
Solución
Ha introducido
[src]
/ x\
\(2*E) /
(cot(3*x))
$$\cot^{\left(2 e\right)^{x}}{\left(3 x \right)}$$
cot(3*x)^((2*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 / 2 \ \
\(2*E) / |(2*E) *\-3 - 3*cot (3*x)/ x |
(cot(3*x)) *|------------------------- + (2*E) *log(2*E)*log(cot(3*x))|
\ cot(3*x) /
$$\left(\frac{\left(2 e\right)^{x} \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right)}{\cot{\left(3 x \right)}} + \left(2 e\right)^{x} \log{\left(2 e \right)} \log{\left(\cot{\left(3 x \right)} \right)}\right) \cot^{\left(2 e\right)^{x}}{\left(3 x \right)}$$
Segunda derivada
[src]
/ 2 2 \
/ x\ | / / 2 \\ / 2 \ / 2 \ |
x \(2*E) / | 2 x | 3*\1 + cot (3*x)/| 2 9*\1 + cot (3*x)/ 6*\1 + cot (3*x)/*log(2*E)|
(2*E) *(cot(3*x)) *|18 + 18*cot (3*x) + (2*E) *|-log(2*E)*log(cot(3*x)) + -----------------| + log (2*E)*log(cot(3*x)) - ------------------ - --------------------------|
| \ cot(3*x) / 2 cot(3*x) |
\ cot (3*x) /
$$\left(2 e\right)^{x} \left(\left(2 e\right)^{x} \left(\frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - \log{\left(2 e \right)} \log{\left(\cot{\left(3 x \right)} \right)}\right)^{2} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} - \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 e \right)}}{\cot{\left(3 x \right)}} + \log{\left(2 e \right)}^{2} \log{\left(\cot{\left(3 x \right)} \right)} + 18 \cot^{2}{\left(3 x \right)} + 18\right) \cot^{\left(2 e\right)^{x}}{\left(3 x \right)}$$
Tercera derivada
[src]
/ 3 3 2 2 / 2 \\
/ x\ | / / 2 \\ / 2 \ / 2 \ / 2 \ 2 / 2 \ / / 2 \\ | / 2 \ / 2 \ ||
x \(2*E) / | 3 2*x | 3*\1 + cot (3*x)/| / 2 \ 54*\1 + cot (3*x)/ / 2 \ 108*\1 + cot (3*x)/ 27*\1 + cot (3*x)/ *log(2*E) 9*log (2*E)*\1 + cot (3*x)/ x | 3*\1 + cot (3*x)/| | 2 2 9*\1 + cot (3*x)/ 6*\1 + cot (3*x)/*log(2*E)||
(2*E) *(cot(3*x)) *|log (2*E)*log(cot(3*x)) - (2*E) *|-log(2*E)*log(cot(3*x)) + -----------------| - 108*\1 + cot (3*x)/*cot(3*x) - ------------------- + 54*\1 + cot (3*x)/*log(2*E) + -------------------- - ---------------------------- - --------------------------- + 3*(2*E) *|-log(2*E)*log(cot(3*x)) + -----------------|*|-18 - 18*cot (3*x) - log (2*E)*log(cot(3*x)) + ------------------ + --------------------------||
| \ cot(3*x) / 3 cot(3*x) 2 cot(3*x) \ cot(3*x) / | 2 cot(3*x) ||
\ cot (3*x) cot (3*x) \ cot (3*x) //
$$\left(2 e\right)^{x} \left(- \left(2 e\right)^{2 x} \left(\frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - \log{\left(2 e \right)} \log{\left(\cot{\left(3 x \right)} \right)}\right)^{3} + 3 \left(2 e\right)^{x} \left(\frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - \log{\left(2 e \right)} \log{\left(\cot{\left(3 x \right)} \right)}\right) \left(\frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} + \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 e \right)}}{\cot{\left(3 x \right)}} - \log{\left(2 e \right)}^{2} \log{\left(\cot{\left(3 x \right)} \right)} - 18 \cot^{2}{\left(3 x \right)} - 18\right) - \frac{54 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3}}{\cot^{3}{\left(3 x \right)}} + \frac{108 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot{\left(3 x \right)}} - \frac{27 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(2 e \right)}}{\cot^{2}{\left(3 x \right)}} - 108 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} + 54 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 e \right)} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 e \right)}^{2}}{\cot{\left(3 x \right)}} + \log{\left(2 e \right)}^{3} \log{\left(\cot{\left(3 x \right)} \right)}\right) \cot^{\left(2 e\right)^{x}}{\left(3 x \right)}$$
Gráfico