Sr Examen
¿Cómo vas a descomponer esta exp(-x)/(1+E^(-x))^2 expresión en fracciones?
Solución
Ha introducido
[src]
-x
e
----------
2
/ -x\
\1 + E /
$$\frac{e^{- x}}{\left(1 + e^{- x}\right)^{2}}$$
exp(-x)/(1 + E^(-x))^2
Descomposición de una fracción
[src]
1/(1 + exp(x)) - 1/(1 + exp(x))^2
$$\frac{1}{e^{x} + 1} - \frac{1}{\left(e^{x} + 1\right)^{2}}$$
1 1
------ - ---------
x 2
1 + e / x\
\1 + e /
Simplificación general
[src]
1
----------
2/x\
4*cosh |-|
\2/
$$\frac{1}{4 \cosh^{2}{\left(\frac{x}{2} \right)}}$$
1/(4*cosh(x/2)^2)
Denominador racional
[src]
x
e
---------
2
/ x\
\1 + e /
$$\frac{e^{x}}{\left(e^{x} + 1\right)^{2}}$$
exp(x)/(1 + exp(x))^2
Denominador común
[src]
x
e
---------------
x 2*x
1 + 2*e + e
$$\frac{e^{x}}{e^{2 x} + 2 e^{x} + 1}$$
exp(x)/(1 + 2*exp(x) + exp(2*x))
Respuesta numérica
[src]
exp(-x)/(1.0 + 2.71828182845905^(-x))^2
exp(-x)/(1.0 + 2.71828182845905^(-x))^2
Unión de expresiones racionales
[src]
x
e
---------
2
/ x\
\1 + e /
$$\frac{e^{x}}{\left(e^{x} + 1\right)^{2}}$$
exp(x)/(1 + exp(x))^2
Parte trigonométrica
[src]
-(-cosh(x) + sinh(x))
------------------------
2
(1 - sinh(x) + cosh(x))
$$- \frac{\sinh{\left(x \right)} - \cosh{\left(x \right)}}{\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)} + 1\right)^{2}}$$
-(-cosh(x) + sinh(x))
----------------------------
2
/ -x\
\1 + (cosh(1) + sinh(1)) /
$$- \frac{\sinh{\left(x \right)} - \cosh{\left(x \right)}}{\left(1 + \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{- x}\right)^{2}}$$
-sinh(x) + cosh(x)
------------------------
2
(1 - sinh(x) + cosh(x))
$$\frac{- \sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)} + 1\right)^{2}}$$
-sinh(x) + cosh(x)
----------------------------
2
/ -x\
\1 + (cosh(1) + sinh(1)) /
$$\frac{- \sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(1 + \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{- x}\right)^{2}}$$
(-sinh(x) + cosh(x))/(1 + (cosh(1) + sinh(1))^(-x))^2
Combinatoria
[src]
x
e
---------
2
/ x\
\1 + e /
$$\frac{e^{x}}{\left(e^{x} + 1\right)^{2}}$$
exp(x)/(1 + exp(x))^2