Question

Suppose g(4) = 4, g'(4) = −2 and f(x) =g(x)/x.
Find f'(4).

Answer 1

From f(x)=g(x)/x, find g'(x).
f'(x)
=(d/dx)(g(x)*x^-1)
=g'(x)/x+g(x)(-x^-2)
=g'(x)/x - g(x)/x^2
so
f'(4)=g'(4)/4-g(4)/4^2
=-2/4-4/16
=-3/4

Check my arithmetic, my eyes are barely open.