# Continuously differentiable

1. Apr 26, 2009

### bubblesewa

1. The problem statement, all variables and given/known data

Suppose that the function f: R^n --> R is continuously differentiable. Let x be a point in R^n. For p a nonzero point in R^n and alpha a nonzero real number, show that
(df/d(alphap))(x)=alpha(df/d(p))(x)

2. Relevant equations

A function f: I --> R, defined on an open interval, is called continuously differentiable provided that it is differentiable and its derivative is continuous.

3. The attempt at a solution

Unfortunately, I do not have one. Which is why I am in dire need of help. I don't know where to begin. By the way, sorry for the horrible formatting, I am new to the forums.

Edit: Okay, I might have an attempt at a solution.

Last edited: Apr 26, 2009
2. Apr 26, 2009

### Dick

If df/d(p) means the directional derivative of f in the direction p, I think that looks ok.

3. Apr 26, 2009

### bubblesewa

Oh, sorry. Yeah. I was talking about the directional derivative. I don't know how to write the actual notation for directional derivatives on here. And thank you for your help!