I've been asked to find the partial derivative with respect to x for the function:

I've learnt about treating y as though it's a constant, and this is what I've got so far. However, I think my working is wrong or my rules haven't been applied correctly. My logic was to apply the product rule to the first grouping, treat e^y just as a constant and just differentiate the last grouping based on the rules for sinh. Here's the result I got:

Hopefully someone can shed some light on whether the working/answer is correct? I'm not feeling very confident about it.