I am in the section of the textbook on derivations using product/ quotient rules. But I don't understand this problem it's asking.
Use the Product Rule to show that (f^2)' = 2ff '.
I've tried just working it through. It doesn't seem to provide any useful insight, or come to f^2'.
f 'f ' + 2f*f ''
f '^2 + 2ff ''
and the other side is just 2f
it is just the chain rule: $$((f(x))^2)'=2f(x)f'(x)$$ or you can take the product rule: $$(f(x)\cdot f(x))'=f'(x)f(x)+f(x)f'(x)$$