I don't want to type this out, so I took a picture of it.

I don't understand the beginning differentiating part. [Why f(x) x f'(y)]

How does letting y=0 give you f'(y)=A (I know A is just a variable, using that as a value of something)

How does f'(x)=Af(x)?

I don't get the substituting x=y=0 part on the bottom, why x=y=0?