# Math Help - Frechet Derivative

1. ## Frechet Derivative

I'm trying to prove that f(r,s)=(r*cos(s),r*sin(s)) is differentiable using the definition of the Frechet derivative, that is:

$\lim_{h \to 0} \frac{ \| f(x + h) - f(x) - L*h \|}{ \|h\|} = 0$

I know how to calculate the Frechet derivative, but I'm not sure how to "show that it's differentiable" using the above definition.

2. Write:

$Lh=\begin{pmatrix}{\cos s_0}&{-r_0\sin s_0}\\{\sin s_0}&{\;\;\;r_0\cos s_0}\end{pmatrix}\left({\begin{array}{ccc}{h_1}\\{ h_2}\end{array}\right)$

an compute the respective norms.

Regards.

Fernando Revilla