Effortlessly Solve C^{2} Functions with Quick and Simple Tips | Get Help Now!

[coolalac]

HELP PLEASE! Quick and simple!

Hey I was wondering if you'll could help. I was told that this is a simple proof but have been working on it for ages and can't get it:

Suppose u is a $$C^{2}$$ function in $$R^{n}$$. Given an nxn matrix, A define v(x):= u(Ax). Show that ($$\nabla$$v)(x) = $$A^{T}$$ . $$\nabla$$u(Ax)

(Note the grad u(Ax) isn't supposed to be superscripted I just don't know how to put it in the same line!)

Pleaseeee help!
Thanks

 

[HallsofIvy]

Hey I was wondering if you'll could help. I was told that this is a simple proof but have been working on it for ages and can't get it:

Suppose u is a $$C^{2}$$ function in $$R^{n}$$. Given an nxn matrix, A define v(x):= u(Ax). Show that ($$\nabla$$v)(x) = $$A^{T}$$ . $$\nabla$$u(Ax)

(Note the grad u(Ax) isn't supposed to be superscripted I just don't know how to put it in the same line!)

You put every thing on the same line by putting the entire formula inside [ tex ] and [ /tex ], not just bits and pieces:
$$\nabla v(x)= A^T\nambla u(Ax)$$
Much simpler to write and to read!

Pleaseeee help!
Thanks

It is, essentially, the "chain rule". v(x)= u(Ax) so $\nabla v(x)= \nabla u(x) d(Ax)/dt= \nabla u(x) A = A^T \nabla u(x)$.