So I'm fairly new to this and I just wanted to check my understanding of the chain rule.
Suppose $f(x) = (ax + b)^n$ and we want to find $f'(x)$. We first work out the derivative of the first function, then multiply it to the derivative of the second function giving:
To calculate the derivative of the second function, we use the sum rule, but this is where I get a little stuck. I know I have to find both $ax'$ and $b'$, so here's how I think I should do it...please tell me if I'm crazy and wrong:
As $b$ is a constant it follows that $b' = 0$. My textbook hasn't gone into this yet, so it isn't clear why. Anyway, moving on. This leaves us with:
$$ax' = a$$
What I REALLY don't understand is why we don't use the product rule for $ax$. Any clues?