remember the quotient rule
[tex] \frac{dy}{dx} \frac{f(x)}{g(x)}= \frac{f'(x)g(x)-g'(x)f(x)}{g(x)^2} [/tex]
k, so
top is 3x^2-8x+4, the deritivive of that is 6x-8
bottom is 7x^2+6x+9, deritivive is 14x+6
so
[tex] \frac{dy}{dx} \frac{top}{bottom}= \frac{top'bottom-bottom'top}{bottom^2}= \frac{(6x-8)(7x^2+6x+9)-(14x+6)(3x^2-8x+4)}{(7x^2+6x+9)^2}[/tex]
if we simplify it we get
[tex] \frac{2(37x^2-x-48)}{(7x^2+6x+9)^2} [/tex]
subsituting x=4
[tex] \frac{216}{4205} [/tex]
