Question

suppose that f(x) and g(x) are differentiable functions such that f(8)=9, f'(8)=4, g(8)=7, and g'(8)=3. Find h'(8) when h(x)=f(x)/g(x).
h'(8)=?? PLEASE HELP MEEE

Answer 1

@zepdrix

Answer 2

\[\Large h(x)\quad=\quad \frac{f(x)}{g(x)}\]
\[\Large h'\quad=\quad \frac{\color{royalblue}{f'}g-f\color{royalblue}{g'}}{g^2}\]Quotient rule for h'(x), yes? :)

Answer 3

\[\Large h'(8)\quad=\quad \frac{\color{royalblue}{f'(8)}g(8)-f(8)\color{royalblue}{g'(8)}}{[g(8)]^2}\]

Answer 4

So we just need to plug a bunch of numbers in, they gave you all the pieces that you need :D

Answer 5

how do I plug what they gave me into that? it's confusing me because they give what like f(8) and f'(8) as well as g not just f(x) and g(x)

Answer 6

Here is how we would plug in one of the pieces of information:
\[\Large \color{royalblue}{f'(8)=4}\]
Plugging in gives us:\[\Large h'(8)\quad=\quad \frac{\color{royalblue}{(4)}g(8)-f(8)\color{royalblue}{g'(8)}}{[g(8)]^2}\]

Answer 7

would it be 28-27/7^2 !? :D

Answer 8

1/7^2 :)

Answer 9

Mmm yah that sounds right!

Answer 10

AHHH awwesome :D thank you!!!

Answer 11

yay team \c:/