Homotopy type of embeddings from the unit ball to $X$.

Question

I read in a paper the following sentence "an embedding of $B$ (the unit ball) is determined by its derivative at a point in $B$ by the inverse function theorem, and so $Emb(B,X)$ is equivalent to the space of injective linear maps $\mathbb{R}^m\to\mathbb{R}^n$. I don't see how does this follow. I know it has something to do with Alexander's trick but i do not get to fix it. Thanks in advance.