# Directional Derivatives

**URL:** <https://community.wolfram.com/t/directional-derivatives/5265>\
**Category:** Questions\
**Created:** [March 28, 2015, 6:43am UTC](https://community.wolfram.com/t/directional-derivatives/5265 "2015-03-28T06:43:52Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![cjf279](https://avatars.discourse-cdn.com/v4/letter/c/ec9cab/32.png) [@cjf279](https://community.wolfram.com/u/cjf279)\
**Post date:** [March 28, 2015, 6:43am UTC](https://community.wolfram.com/t/directional-derivatives/5265/1 "2015-03-28T06:43:52Z")

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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