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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
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monotonicity of a function
I want to know if the function below is monotonically decreasing for all $a,b >0, a\neq b $
\begin{equation}
x\rightarrow \frac{\sinh^2((a-b)x)}{\sinh(2ax)\sinh(2bx)} \text{, $x >0. $}
\end{equation …