What is this question asking in laymans terms?

Question

I am very new to proofs, and such, and I came across this question. I know what surjective and injective mean, but I don't understand what the question is even asking..

here it is.

Answer 1

$\frac{d}{dx}$ is a function that maps $P$ to $P$.

Hence the question if $\frac{d}{dx}$ is injective means, suppose we have $p,q \in P$ such that $\frac{d}{dx}p=\frac{d}{dx}q$, can you conclude that $p=q$?

The question is asking is it possible for two different functions to have the same derivative.