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=(ctg5x)^sin2x
- y es igual a (ctg5x) en el grado seno de 2x
- y=(ctg5x)sin2x
- y=ctg5xsin2x
- y=ctg5x^sin2x
Derivada de y=(ctg5x)^sin2x
Solución
Ha introducido
[src]
sin(2*x) cot (5*x)
$$\cot^{\sin{\left(2 x \right)}}{\left(5 x \right)}$$
cot(5*x)^sin(2*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 \ \
sin(2*x) | \-5 - 5*cot (5*x)/*sin(2*x)|
cot (5*x)*|2*cos(2*x)*log(cot(5*x)) + ---------------------------|
\ cot(5*x) /
$$\left(\frac{\left(- 5 \cot^{2}{\left(5 x \right)} - 5\right) \sin{\left(2 x \right)}}{\cot{\left(5 x \right)}} + 2 \log{\left(\cot{\left(5 x \right)} \right)} \cos{\left(2 x \right)}\right) \cot^{\sin{\left(2 x \right)}}{\left(5 x \right)}$$
Segunda derivada
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
sin(2*x) || 5*\1 + cot (5*x)/*sin(2*x)| / 2 \ 25*\1 + cot (5*x)/ *sin(2*x) 20*\1 + cot (5*x)/*cos(2*x)|
cot (5*x)*||-2*cos(2*x)*log(cot(5*x)) + --------------------------| - 4*log(cot(5*x))*sin(2*x) + 50*\1 + cot (5*x)/*sin(2*x) - ---------------------------- - ---------------------------|
|\ cot(5*x) / 2 cot(5*x) |
\ cot (5*x) /
$$\left(\left(\frac{5 \left(\cot^{2}{\left(5 x \right)} + 1\right) \sin{\left(2 x \right)}}{\cot{\left(5 x \right)}} - 2 \log{\left(\cot{\left(5 x \right)} \right)} \cos{\left(2 x \right)}\right)^{2} - \frac{25 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\cot^{2}{\left(5 x \right)}} + 50 \left(\cot^{2}{\left(5 x \right)} + 1\right) \sin{\left(2 x \right)} - \frac{20 \left(\cot^{2}{\left(5 x \right)} + 1\right) \cos{\left(2 x \right)}}{\cot{\left(5 x \right)}} - 4 \log{\left(\cot{\left(5 x \right)} \right)} \sin{\left(2 x \right)}\right) \cot^{\sin{\left(2 x \right)}}{\left(5 x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 3 2 2 \
| / / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
sin(2*x) | | 5*\1 + cot (5*x)/*sin(2*x)| | 5*\1 + cot (5*x)/*sin(2*x)| | / 2 \ 20*\1 + cot (5*x)/*cos(2*x) 25*\1 + cot (5*x)/ *sin(2*x)| / 2 \ / 2 \ 250*\1 + cot (5*x)/ *sin(2*x) 150*\1 + cot (5*x)/ *cos(2*x) 60*\1 + cot (5*x)/*sin(2*x) 500*\1 + cot (5*x)/ *sin(2*x)|
cot (5*x)*|- |-2*cos(2*x)*log(cot(5*x)) + --------------------------| - 8*cos(2*x)*log(cot(5*x)) + 3*|-2*cos(2*x)*log(cot(5*x)) + --------------------------|*|- 50*\1 + cot (5*x)/*sin(2*x) + 4*log(cot(5*x))*sin(2*x) + --------------------------- + ----------------------------| + 300*\1 + cot (5*x)/*cos(2*x) - 500*\1 + cot (5*x)/*cot(5*x)*sin(2*x) - ----------------------------- - ----------------------------- + --------------------------- + -----------------------------|
| \ cot(5*x) / \ cot(5*x) / | cot(5*x) 2 | 3 2 cot(5*x) cot(5*x) |
\ \ cot (5*x) / cot (5*x) cot (5*x) /
$$\left(- \left(\frac{5 \left(\cot^{2}{\left(5 x \right)} + 1\right) \sin{\left(2 x \right)}}{\cot{\left(5 x \right)}} - 2 \log{\left(\cot{\left(5 x \right)} \right)} \cos{\left(2 x \right)}\right)^{3} + 3 \left(\frac{5 \left(\cot^{2}{\left(5 x \right)} + 1\right) \sin{\left(2 x \right)}}{\cot{\left(5 x \right)}} - 2 \log{\left(\cot{\left(5 x \right)} \right)} \cos{\left(2 x \right)}\right) \left(\frac{25 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\cot^{2}{\left(5 x \right)}} - 50 \left(\cot^{2}{\left(5 x \right)} + 1\right) \sin{\left(2 x \right)} + \frac{20 \left(\cot^{2}{\left(5 x \right)} + 1\right) \cos{\left(2 x \right)}}{\cot{\left(5 x \right)}} + 4 \log{\left(\cot{\left(5 x \right)} \right)} \sin{\left(2 x \right)}\right) - \frac{250 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{3} \sin{\left(2 x \right)}}{\cot^{3}{\left(5 x \right)}} + \frac{500 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\cot{\left(5 x \right)}} - \frac{150 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2} \cos{\left(2 x \right)}}{\cot^{2}{\left(5 x \right)}} - 500 \left(\cot^{2}{\left(5 x \right)} + 1\right) \sin{\left(2 x \right)} \cot{\left(5 x \right)} + \frac{60 \left(\cot^{2}{\left(5 x \right)} + 1\right) \sin{\left(2 x \right)}}{\cot{\left(5 x \right)}} + 300 \left(\cot^{2}{\left(5 x \right)} + 1\right) \cos{\left(2 x \right)} - 8 \log{\left(\cot{\left(5 x \right)} \right)} \cos{\left(2 x \right)}\right) \cot^{\sin{\left(2 x \right)}}{\left(5 x \right)}$$
Gráfico