Finding the derivative of a function using the Product Rule I'm home teaching myself calculus because I'm 16 and therefore too young to take an actual class with a teacher, so I apologise if this seems simple.
I understand the definition of the Product Rule and its formula:

"If a function $h(x)=f(x)\times g(x)$ is the product of two differentiable functions $f(x)$ and $g(x)$, then $h'(x) = f(x)\times g'(x)+f'(x)\times g(x)$".

I did a question to find the derivative of $g(x) = (2x+1)(x+4)$ using the Product Rule.
Now on the solutions sheet it says I must begin by writing:
$g'(x)=(2x+1){\bf (1)}+{\bf (2)}(x+4)$
What confuses me are the terms that I have put in bold. (the terms $(1)$ and $(2)$). I believe the term $(1)$ is $g'(x)$ from the formula and the term $(2)$ is $f'(x)$ from the formula. 
How am I supposed to know these 2 terms? Am I supposed to find the derivative of $(2x+1)$ and $(x+4)$ before going on to the question?
I also apologise if this is quite messy.

You’re supposed to find the derivatives of $2x+1$ and $x+4$ as part of finding the derivative of their product:
$$\begin{align*}
\Big((2x+1)(x+4)\Big)'&=(2x+1)(x+4)'+(x+4)(2x+1)'\\
&=(2x+1)(1)+(x+4)(2)\\
&=(2x+1)+(2x+8)\\
&=4x+9\;.
\end{align*}$$
Note that you can check this by multiplying out the original function to get $2x^2+9x+4$ and taking its derivative directly.
