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
-
¿Cómo usar?
- Derivada de:
-
Derivada de (-4)/x^2
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Derivada de 2/x²
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Derivada de -2*y
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Derivada de (3+2x)/(x-5)
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Expresiones idénticas
- y=arctancsch(cotx)
- y es igual a arc tangente de csch( cotangente de x)
- y=arctancschcotx
Derivada de y=arctancsch(cotx)
Solución
Ha introducido
[src]
atan(csch(cot(x)))
$$\operatorname{atan}{\left(\operatorname{csch}{\left(\cot{\left(x \right)} \right)} \right)}$$
atan(csch(cot(x)))
Primera derivada
[src]
/ 2 \
-\-1 - cot (x)/*coth(cot(x))*csch(cot(x))
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2
1 + csch (cot(x))
$$- \frac{\left(- \cot^{2}{\left(x \right)} - 1\right) \coth{\left(\cot{\left(x \right)} \right)} \operatorname{csch}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1}$$
Segunda derivada
[src]
/ 2 2 2 / 2 \\
/ 2 \ | 2 / 2 \ 1 + cot (x) 2*coth (cot(x))*csch (cot(x))*\1 + cot (x)/|
\1 + cot (x)/*|coth (cot(x))*\1 + cot (x)/ + ------------- - 2*cot(x)*coth(cot(x)) - -------------------------------------------|*csch(cot(x))
| 2 2 |
\ sinh (cot(x)) 1 + csch (cot(x)) /
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2
1 + csch (cot(x))
$$\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \left(\left(\cot^{2}{\left(x \right)} + 1\right) \coth^{2}{\left(\cot{\left(x \right)} \right)} + \frac{\cot^{2}{\left(x \right)} + 1}{\sinh^{2}{\left(\cot{\left(x \right)} \right)}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \coth^{2}{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1} - 2 \cot{\left(x \right)} \coth{\left(\cot{\left(x \right)} \right)}\right) \operatorname{csch}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1}$$
Tercera derivada
[src]
/ 2 2 2 2 2 \
| 2 / 2 \ / 2 \ / 2 \ / 2 \ 3 2 / 2 \ 3 4 / 2 \ 2 2 2 / 2 \ |
/ 2 \ |/ 2 \ 3 / 2 \ 2 2 / 2 \ 6*\1 + cot (x)/*cot(x) 2*\1 + cot (x)/ *cosh(cot(x)) 3*\1 + cot (x)/ *coth(cot(x)) 8*\1 + cot (x)/ *coth (cot(x))*csch (cot(x)) 8*\1 + cot (x)/ *coth (cot(x))*csch (cot(x)) 6*\1 + cot (x)/ *csch (cot(x))*coth(cot(x)) 12*coth (cot(x))*csch (cot(x))*\1 + cot (x)/*cot(x)|
\1 + cot (x)/*|\1 + cot (x)/ *coth (cot(x)) + 2*\1 + cot (x)/*coth(cot(x)) + 4*cot (x)*coth(cot(x)) - 6*coth (cot(x))*\1 + cot (x)/*cot(x) - ---------------------- + ----------------------------- + ----------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + ---------------------------------------------------|*csch(cot(x))
| 2 3 2 2 2 / 2 \ 2 2 |
| sinh (cot(x)) sinh (cot(x)) sinh (cot(x)) 1 + csch (cot(x)) / 2 \ \1 + csch (cot(x))/*sinh (cot(x)) 1 + csch (cot(x)) |
\ \1 + csch (cot(x))/ /
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2
1 + csch (cot(x))
$$\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \left(\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth^{3}{\left(\cot{\left(x \right)} \right)} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth{\left(\cot{\left(x \right)} \right)}}{\sinh^{2}{\left(\cot{\left(x \right)} \right)}} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cosh{\left(\cot{\left(x \right)} \right)}}{\sinh^{3}{\left(\cot{\left(x \right)} \right)}} - \frac{8 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth^{3}{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)}}{\left(\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1\right) \sinh^{2}{\left(\cot{\left(x \right)} \right)}} + \frac{8 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth^{3}{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{4}{\left(\cot{\left(x \right)} \right)}}{\left(\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1\right)^{2}} - 6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \coth^{2}{\left(\cot{\left(x \right)} \right)} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\sinh^{2}{\left(\cot{\left(x \right)} \right)}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \coth{\left(\cot{\left(x \right)} \right)} + \frac{12 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \coth^{2}{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1} + 4 \cot^{2}{\left(x \right)} \coth{\left(\cot{\left(x \right)} \right)}\right) \operatorname{csch}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1}$$
Gráfico