If you're like me and don't remember hyperbolic identities (especially involving inverse functions) off the top of your head, recall the definitions of the hyperbolic cosine and sine:

Then differentiating yields

so that by the chain rule, if

then

Now, let
, so that (•)
.
Recall that

and so the derivative of tanh(<em>x</em>) is

where the last equality follows from the hyperbolic Pythagorean identity,

Differentiating both sides of (•) implicitly with respect to <em>x</em> gives

So, the derivative we want is the somewhat messy expression

and while this could be simplified into a rational expression of <em>x</em>, I would argue for leaving the solution in this form considering how <em>y</em> is given in this form from the start.
In case you are interested, we have

and you can instead work on differentiating that; you would end up with
