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${F(x)} = {f(x)g(x)h(x)}$

The above equation is true for all real $x$, where $f(x)$, $g(x)$ and $h(x)$ are differentiable functions at some point $a$.

Given $F '(a) = 21 F(a), f '(a) = 4f(a), g'(a) = -7g(a), h'(a) = kh(a)$. Find $k$.

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