suppose $k$ is a field and take two polynomials $p(x),g(x) \in k[x]$. If $(p,p')=1$ and $(g,g')=1$ then why is it true that $(pg,(pg)')=1$ where $'$ denotes formal derivative and $(,)$ denotes gcd (i.e (pg)' denotes the derivative of pg). I tried writing the gcd as linear combination and using the chain rule but I don't see it. Can you please help me
Relatively prime polynomials in $k[x]$
3
$\begingroup$
abstract-algebra