[tex]\dfrac{145}{25}[/tex]
Step-by-step explanation:
Recall the product rule of differentiation,
[tex]\dfrac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)[/tex]
Using the quotient rule of differentiation,
[tex]\dfrac{d}{dx}\left[\dfrac{f(x)g(x)}{x}\right] = \dfrac{x\frac{d}{dx}[f(x)g(x)] - f(x)g(x)}{x^2}[/tex]
[tex]\:\:\:\:=\dfrac{xf'(x)g(x) + xf(x)g'(x) - f(x)g(x)}{x^2}[/tex]
Evaluating this expression for x = 5, we get
[tex]\left.\dfrac{d}{dx}\left[\dfrac{f(x)g(x)}{x}\right]\right|_{x=5}[/tex]
[tex]= \dfrac{(5)(5)(5) + (5)(2)(3) - (2)(5)}{25}[/tex]
[tex]\:\:\:\:=\dfrac{145}{25}[/tex]
