Question

If f(3) =0, f'(3) = 6, g(3) = 1 and g'(3) = 1/3, Find h'(3) if h(x) = f(x)/g(x).
My answer is below. Please check if it's correct.

Answer 1

\[h(x) = \frac{ f'(x)g(x) - g'(x)f(x) }{ (g(x))^2 }\]
\[h'(3) = \frac{ f'(3)g(3)-g'(3)f(3) }{ (g(3))^2 }\]
\[h'(3) = \frac{ 6(1) - (\frac{ 1 }{ 3 })(0) }{ (\frac{ 1 }{ 3 })^2 }\]
is the work correct so far?

Answer 2

oh crap. i think i see my mistake.