Simple but nice

Calculus Level 2

\[{F(x)} = {f(x)g(x)h(x)}\]

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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