Let H be a function defined as H(x)= g(x)/h(x). What is H'(4) ?

Question

Let g be a function such that g(4)=16 and g'(4)=12

Let h be the function h(x)=sqrt(x)

Answer 1

H'(x)=(g'(x)h(x)-g(x)h'(x))/h(x)^2

h'(x)=1/(2sqrt(x))

h'(4)=1/4

h(4)=2

H'(x)=(g'(4)2-g(4)/4)/2^2

=(16*2-12/4)/4

=(32-3)/4

=29/4