Proving Continuity of Derivatives for a Multivariable Function

[bubblesewa]

Homework Statement

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)

Homework 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.

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.
(df/d(alphap))(x)=<gradientf(x),alphap>=alpha<gradientf(x),p>=alpha(df/dp)(x)

 

[Dick]

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

 

[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!