Whats the Product rule for differentiation and how does it work?

We use the product rule when we want to find the derivative of a product of two functions using their individual derivatives, the product rule can be written out as the following formula: fg'(x) = f(x)g'(x) + g(x)f'(x)Let's consider an example, remember that practicing on as many different examples as possible is the best way to understand how this rule works as with other rules in general; suppose we are asked the question:Q: Given f(x)=4x and g(x)=x^2 what is the derivative of the fg(x) at x=2 and x=3?A: We first apply the general product rule to find the derivative function and then we plug in x=2 and x=3 to find the derivative at those points, restating the rule and plugging in our functions we have:fg'(x) = f(x)g'(x) + g(x)f'(x) = 4x(x^2)' + x^2(4x)'From the polynomial derivative rule we know that: (x^2)' = 2x and (4x)' = 4 and therefore:fg'(x) = 4x2x + x^24 = 8x^2 + 4x^2 = 12x^2Now that we have our derivative function, we plug in x=2 to get fg'(2)= 12*(2^2)=48 and x=3 to get fg'(3) = 12*(3^2)=108Are there any parts of my explanation that are unclear?