Question

How/why does this equality hold?

Answer 1

\[\frac{f(a+h)g(a+h) - f(a)g(a)}{h}\]
=
\[g(a) \frac{f(a+h)-f(a)}{h} + f(a+h) \frac{g(a+h)-g(a)}{h}\]
where f,g are real functions and a,h are real variables