Every time I feel like I understand it, something new comes up and proves me wrong. I have been given an example in my text and I did the question before looking at the answer. I don't understand why they did it the way they did and I feel like my answer is correct. Clearly I do not understand how to do this right. I was hoping someone could clear things up for me.

My answer:

text answer:

Also, the chain rule I have been given for exponential functions is this:

where a is a positive constant, is given by

, which I paired with the difference rule.

So I guess what I'm really trying to figure out here, is why they put

in front?