Partial Derivatives & the Gradient · Challenge problem

Let $A = (0,0)$ and $B = (6,0)$, and let $f(P) = \lvert PA\rvert + \lvert PB\rvert$ be the sum of the distances from the point $P = (x,y)$ to $A$ and $B$. Find $\lvert\nabla f\rvert$ at $P = (0, 8)$.