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Let $f$ and $g$ be functions from $\mathbb{R}^n \to \mathbb{R}^m$. Assume that $f$ is differentiable at $c$, that $f(c)=0$, and that $g$ is continuous at $c$. Let $h(x)=g(x)f(x)$.

Prove that $h$ is differentiable at $c$ and that $h'(c;u)=g(c)\{f'(c;u)\}$ answer h'(c;u) =lim{ h(c+h1)-h(c)}\h h1->0 =lim {g(c+h1u)f(c+h1u)-g(c)f(c)}\h1 h1->0 =lim {g(c+h1u)f(c+h1u)}\h1 h1->0 =lim g(c+h1u)lim f(c+h1u)\h1 h1->0 h1->0
=g(c)f'(c;u)

AMRJ
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    Writing some context to the task, how far you have gotten yourself, what your thoughts are, where exactly your troubles are and such things make this seem less like a rather rude request for others to do your homework. Just something to think about. – Some Math Student Oct 12 '14 at 13:35

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