Answer
$\frac{13}{250}$
Work Step by Step
Applying the quotient rule, we have
$H'(x)=\frac{\frac{d}{dx}(x)\times g(x) f(x)-x\times\frac{d}{dx}(g(x) f(x))}{(g(x) f(x))^{2}}$
$=\frac{g(x) f(x)-x(g'(x)f(x)+g(x)f'(x))}{(g(x)f(x))^{2}}$
(To find the derivative of $g(x)f(x)$, we applied the product rule)
$H'(4)=\frac{g(4) f(4)-4(g'(4)f(4)+g(4)f'(4))}{(g(4)f(4))^{2}}$
$=\frac{5\times10-4(-1\times10+5\times-2)}{(5\times10)^{2}}=\frac{13}{250}$
