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Directional Derivatives

Posted 9 years ago

Hi Community,

I've just started directional derivatives in calculus, and need to prove the following, and I have no idea where to start.

Let U subset of R^n be open, f:U ---> R^m is a function, a is found in U and 0 does not equal v, which is a vector in R^n such that D(v)f(a) exists. (For typing purposes, & means lambda)

Show that D(&v)f(a) exists for every & that does not equal 0 in R, and show D(&v)f(a) = &D(v)f(a) ----- I know that D(v)f(a) = lim (h-->0) (f(a+h(v)) - f(a)) / h

Thanks

POSTED BY: Claire Fenwicke
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