Let `F(x)=f(x)g(x)h(x)` for all real `x ,w h e r ef(x),g(x),a n dh(x)` are differentiable functions. At some point `x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)4f(x_0),g^(prime)(x_0)=-7g(x_0),` then the value of `g^(prime)(1)` is ________

Explanation

To solve the problem, we start with the function \( F(x) = f(x)g(x)h(x) \) and differentiate it using the product rule.

### Step-by-Step Solution:

1. **Differentiate \( F(x) \)**:
We apply the product rule to differentiate \( F(x) \):
\[
F'(x) = f'(x)g(x)h(x) + f(x)g'(x)h(x) + f(x)g(x)h'(x)
...