Let f be differentiable function such that f(8) =2 and f'(8) =5. If gis the function defined by g(x)= f(x)/ x√3, what is the value of g'(8)?

Question

A. 59/24

B. 5/2

C. 61/24

D. 60

Answer 1

Lets do a few things first. First, lets define x√3 as h(x). Then we get that g(x) = f(x)/h(x), which means if we want to take the derivative of g, we have to use the quotient rule, which is as follows: g'(x) = (f'(x)h(x) - h'(x)f(x))/[h'(x)]². This implies that: g'(8) = (f'(8)h(8) - h'(8)f(8))/[h'(8)]² .Since h(x) = x√3, h'(x) = √3 . Also h(8) = 8√3 and h'(8) = √3. Plugging in the values we were given, we get that g'(8) = (5*8√3 - (√3)*2)/(√3)² = (40√3 - 2√3)/3 = (38√3)/3