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:
-
Derivada de (-4)/x^2
-
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=arctg^ dos (sh2x)
- y es igual a arctg al cuadrado (sh2x)
- y es igual a arctg en el grado dos (sh2x)
- y=arctg2(sh2x)
- y=arctg2sh2x
- y=arctg²(sh2x)
- y=arctg en el grado 2(sh2x)
- y=arctg^2sh2x
Derivada de y=arctg^2(sh2x)
Solución
Ha introducido
[src]
2 atan (sinh(2*x))
$$\operatorname{atan}^{2}{\left(\sinh{\left(2 x \right)} \right)}$$
atan(sinh(2*x))^2
Primera derivada
[src]
4*atan(sinh(2*x))*cosh(2*x)
---------------------------
2
1 + sinh (2*x)
$$\frac{4 \cosh{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\sinh^{2}{\left(2 x \right)} + 1}$$
Segunda derivada
[src]
/ 2 2 \
| cosh (2*x) 2*cosh (2*x)*atan(sinh(2*x))*sinh(2*x)|
8*|-------------- + atan(sinh(2*x))*sinh(2*x) - --------------------------------------|
| 2 2 |
\1 + sinh (2*x) 1 + sinh (2*x) /
---------------------------------------------------------------------------------------
2
1 + sinh (2*x)
$$\frac{8 \left(\sinh{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)} - \frac{2 \sinh{\left(2 x \right)} \cosh^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\sinh^{2}{\left(2 x \right)} + 1} + \frac{\cosh^{2}{\left(2 x \right)}}{\sinh^{2}{\left(2 x \right)} + 1}\right)}{\sinh^{2}{\left(2 x \right)} + 1}$$
Tercera derivada
[src]
/ 2 2 2 2 2 \
| 3*sinh(2*x) 6*sinh (2*x)*atan(sinh(2*x)) 6*cosh (2*x)*sinh(2*x) 2*cosh (2*x)*atan(sinh(2*x)) 8*cosh (2*x)*sinh (2*x)*atan(sinh(2*x)) |
16*|-------------- - ---------------------------- - ---------------------- - ---------------------------- + --------------------------------------- + atan(sinh(2*x))|*cosh(2*x)
| 2 2 2 2 2 |
|1 + sinh (2*x) 1 + sinh (2*x) / 2 \ 1 + sinh (2*x) / 2 \ |
\ \1 + sinh (2*x)/ \1 + sinh (2*x)/ /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
1 + sinh (2*x)
$$\frac{16 \left(\operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)} - \frac{6 \sinh^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\sinh^{2}{\left(2 x \right)} + 1} + \frac{3 \sinh{\left(2 x \right)}}{\sinh^{2}{\left(2 x \right)} + 1} - \frac{2 \cosh^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\sinh^{2}{\left(2 x \right)} + 1} + \frac{8 \sinh^{2}{\left(2 x \right)} \cosh^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\left(\sinh^{2}{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \sinh{\left(2 x \right)} \cosh^{2}{\left(2 x \right)}}{\left(\sinh^{2}{\left(2 x \right)} + 1\right)^{2}}\right) \cosh{\left(2 x \right)}}{\sinh^{2}{\left(2 x \right)} + 1}$$
Gráfico