This forum is such a good resource - I have another question regarding implicit differentiation that I can't find any information in my notes for.

I have the following question...

Assume x and y are functions of t. Evaluate for the following.

What I'm a little unsure about, is that when working through this, mainly when using the chain rule for exponential functions when trying to find

I got up to about the second step shown below, but then realized that something isn't right at all. I completed the equation to it's (incorrect) conclusion, but I don't really no how to handle the exponents and Euler's number when working with it.

=

I'm pretty sure that I've already made a mistake somewhere along the line here, but just to make sure...

Which is just ridiculous...