How would you show that for the directional derivative $D_vf(p)$ of $f$ at location $p$ with respect to $v$ the following formula holds for $c \in \mathbb{R}$ $$D_{cv}f(p) = cD_vf(p)\, ?$$
A formula involving the directional derivative
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real-analysis
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0As a hint: consider that the directional derivative is the dot product of v with the gradient of f evaluated at p, and then think about what properties of the dot product you know. It may help to write out an explicit example in order to visualize it. – 2012-05-17
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0@AlexP: That is only true if the gradient of $f$ at $p$ exists. – 2012-06-18