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Let be $f:\mathbb{R}^N\rightarrow \mathbb{R}$. Let be $r$ a vector function, such that $r:\mathbb{R}\rightarrow \mathbb{R}^N$. Making $r(t)=y$ and $g(t)=f[r(t)]$. My lecture say: $g'(t)=\nabla f(y)r'(t)$.

But I think that expression need something. Because, appying chain rule I get

$g'(t)=\dfrac{\partial f}{\partial y}r'(t)=(\nabla f(y) \cdot n )(r'(t))$ or not?

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    What is $n$ supposed to represent?2012-11-10

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