Re: calc question ,

On Thu, 23 Mar 2006 10:48:08 -0800, "quat" <spam@xxxxxxxx> wrote:

I am trying to show:

g(x,y,z) = I( g(xt, yt, zt), t, 0, 1) + I( [x*g_x(xt, yt, zt) + y*g_y(xt,
yt,zt) + z*g_z(xt, yt, zt)]t, t, 0, 1),

where I( f, x, 0, 1) means integral of f wrt x from 0 to 1. The book says
to differentiate t*g(xt, yt, zt) to see this. From the product rule I got:

(tg)' = g + tg'

If you write it out with all the arguments, what you have so far,
which is correct, is:

( tg(xt, yt, zt) )' = g(xt, yt, zt) + t g'(xt, yt, zt)

where ' denotes d/dt. Now you need to use the chain rule to expand
that last g'. Does that help?

--Lynn
.

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