For which $d$ values does the equation $x - d\tanh(x) = 0$ have a positive solution?
I have tried rearranging this a number of different ways using the exponential form and and using hyperbolic trig identities but I am not entirely sure what I am looking for exactly.
Am I trying to find a positive solution for $x=d\tanh(x)$? How am I supposed to relate $d$ and $x$?
EDIT: I have a provided answer of $d = \frac{1}{\operatorname{sech}^2(x)} > 1$.