\(F'(x)=\lim_{h\to 0}\frac{f(x+h)\cdot g(x+h)-f(x)g(x+h)+f(x)g(x+h)-f(x)g(x)}{h}\Longrightarrow\lim_{h\to 0}\frac{[f(x+h)-f(x)]g(x+h)+f(x)[g(x+h)-g(x)]}{h}\)