# Differentiability and least squares

Here is an interesting problem I encountered in Mike Wilson’s analysis course: let $$u \in \mathbb{R}^d$$ be a unit vector and define the function $$f: \mathbb{R}^d \rightarrow \mathbb{R}$$ by

Show that $$f$$ is differentiable on all of $$\mathbb{R}^d$$, and find an expression for $$f’(p)$$ in terms of $$p$$ and $$u$$.

Check it out here!

N.B.: Professor Wilson’s class is quite hard (this is one of the easier problems he assigned in the second half of the semester) but well worth the effort. I highly recommend it to any interested student.

Written on June 30, 2017