Find the derivative of f(x) = negative 9 divided by x at x = 6. 2 divided by 3 1 divided by 4 3 divided by 2 4

300 jelly beans cost you x dollars.
if you divide 300 by x, you get the number of jelly beans per dollar.
now you are buying 1/2 a dollar's worth of jelly beans, so you will be getting 1/2 * 300 / x which is equal to 150 / x jelly beans.
the actual number of jelly beans you get is determined by x.
if x = 1, the you get 150 jelly beans for 1/2 of a dollar.
if x = 3, then you get 50 jelly beans for 1/2 of a dollar.

you can also work this out by determing the cost per jelly bean.
if you pay x dollars for 300 jelly beans, then the cost per jelly bean is equal to x/300.
now you want to buy 50 cents worth of jelly beans.
the number of jelly beans you can buy is the money you pay divided by the cost per jelly bean.
you pay 50 cents which is equal to 1/2 of a dollar.
you will get 1/2 / (x/300) which is equal to ((1/2)*300)/x which is equal to 150/x.
now let's assume x is equal to 1.
you will get 150/1 = 150 jelly beans.
now let's assume x is equal to 3.
you will get 150/3 = 50 jelly beans.

the equation becomes:
number of jelly beans = 150/x
x = cost for 300 jelly beans.
it's just a matter of how you want to look at it.

another way to look at it would be to set up a ratio.
the ratio would be:
300/x = y/.5
this ratio says:
300 jelly beans is to x dollars as y jelly beans is to half a dollar.
cross multiply to get:
.5*300 = x*y

simplify to get:
150 = x*y
divide both sides of the equation by x to get:
y = 150/x
same equation again.
x is the cost for 300 jelly beans.
y is the number of jelly beans you can get for half a dollar.