Suppose that $f(5) = 1$, $f'(5) = 9$, $g(5) = -4$, and $g'(5) = 7$. Find the following values.
(a) $(fg)'(5)$
(b) $(f/g)'(5)$
(c) $(g/f)'(5)$
Please try again. You have to use either the Product Rule or the Quotient Rule to solve these problems. To apply the Product Rule, first identify the two factors of the product as $f(x)g(x)$, and then use the form
the Quotient Rule, first identify the numerator and denominator in the quotient $\frac{f(x)}{g(x)}$, then use the formula
$$\frac{d}{dx}\left[\frac{f(x)}{g(x)}\right] = \frac{g(x)\frac{d}{dx}[f(x)] - f(x)\frac{d}{dx}[g(x)]}{[g(x)]^2}$$
Finally, replace the variable $x$ with the $x$-value of interest.