Derivatives help please: Find d/dx of (f(x)g(x))/x, given x=2, f(2)=3, g(2)=3,...

[awats9]

Find d/dx of (f(x)g(x))/x given
x=2
f(2)=3
g(2)=3
g'(2)=5
f'(2)=2
the answer should be 33/4 but I'm not sure how to get it

I found the derivative of f(x)g(x) using the product rule and then I used the quotient rule (derivative of f(x)g(x)*x - derivative of x*f(x)g(x) all divided by x^2) but my answer was not correct

 

[Deleted member 4993]

Find d/dx of (f(x)g(x))/x given
x=2
f(2)=3
g(2)=3
g'(2)=5
f'(2)=2
the answer should be 33/4 but I'm not sure how to get it

I found the derivative of f(x)g(x) using the product rule and then I used the quotient rule (derivative of f(x)g(x)*x - derivative of x*f(x)g(x) all divided by x^2) but my answer was not correct

\(\displaystyle \displaystyle{\frac{d}{dx}\left [\frac{g(x)*f(x)}{x}\right ]}\)

= \(\displaystyle \displaystyle{\frac{ x*[f(x)*g(x)]' - g(x)*f(x)}{x^2}}\)