Problem with a question requiring me to prove a derivative

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I have been staring at the following question for an hour now, but the answer simply does not make sense to me…

The question asks: please prove that if a is a constant, then... Question

My problem with the answer is that I do not understand where the first ay comes from in the numerator in ay(x+Δx) Answer

Could somebody please help out?

Thanks!

Yair