Question

Use definition of the derivative to prove the formula (fg)' = f'g+fg'

Answer 1

\[\begin{align}
(f(x)g(x))'&=\lim_{h \to 0}\frac{f(x+h)g(x+h)-f(x)g(x)}{h}\\
&=\lim_{h \to 0} \frac{f(x+h)g(x+h)-f(x+h)g(x)+f(x+h)g(x)-f(x)g(x)}{h}\\
&=\lim_{h \to 0} \frac{f(x+h)[g(x+h)-g(x)]}{h}+\lim_{h \to 0}\frac{g(x)[f(x+h)-f(x)]}{h}
\end{align}\]
You can do it from here.

Answer 2

ok thanks you :)