Let $f: \mathbb{R}^n \to \mathbb{R}$. For $x \in \mathbb{R}^n$, the limit $$\lim_{s \to 0} \frac{f(a + sx) - f(a)}{s}$$ if it exists is called the directional derivative of $f$ at $a$ in the direction $x$ and is denoted $D_x f(a)$. I want to show that $D_{tx}f(a) = tD_xf(a)$. Help is appreciated.
Directional derivative question
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multivariable-calculus
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0You seem to be using the variable $t$ in two different contexts. It would be good to have another variable. – 2012-06-13
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0That actually makes things a lot clearer. I was misinterpreting this problem. – 2012-06-13