# Product and Quotient Rule Help

• Feb 18th 2009, 11:52 AM
ANIMAL who
Product and Quotient Rule Help
x-3x(Square root of x)/(square root of x)
or
x-3x(times)sqrt of x/sqrt of x

first solved by using the quotient rule second by simplifying first

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A manufacturer produces bolts of fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write q = f(p). Then the total revenue earned with selling price p is R(p) = pf(p). Given f(18) = 8000 and f'(18) = -320, find R'(18).1

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In this exercise we estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 912,300, and the population was increasing at roughly 9800 per year. The average annual income was $29,001 per capita, and this average was increasing at about$1400 per year (a little above the national average of about $1225 yearly). Use the Product Rule and these figures to estimate the rate at which total personal income was rising in the area in 1999. • Feb 18th 2009, 04:49 PM mollymcf2009 Quote: Originally Posted by ANIMAL who x-3x(Square root of x)/(square root of x) or x-3x(times)sqrt of x/sqrt of x first solved by using the quotient rule second by simplifying first ---------------------------------------------------------------------------------------- A manufacturer produces bolts of fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write q = f(p). Then the total revenue earned with selling price p is R(p) = pf(p). Given f(18) = 8000 and f'(18) = -320, find R'(18).1 ----------------------------------------------------------------------------------------- In this exercise we estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 912,300, and the population was increasing at roughly 9800 per year. The average annual income was$29,001 per capita, and this average was increasing at about $1400 per year (a little above the national average of about$1225 yearly). Use the Product Rule and these figures to estimate the rate at which total personal income was rising in the area in 1999.

Can you confirm that the first one is written like this:

$\displaystyle \frac{x-3x\sqrt x}{\sqrt x}$

Correct?
I'll work on the others
• Feb 18th 2009, 04:54 PM
ANIMAL who
yes the first one is written like that, thanks alot for your help
• Feb 18th 2009, 05:25 PM
mollymcf2009
Quote:

Originally Posted by ANIMAL who
yes the first one is written like that, thanks alot for your help

Ok, sorry I took so long, I'm also doing homework

So we have:

$\displaystyle \frac{x-3x\sqrt x}{\sqrt x} dx$

First simplify the top by writing:

$\displaystyle \frac{x-3x^{\frac{3}{2}}}{\sqrt x} dx$

Then you can split it and use the product rule:
$\displaystyle (x-3x^{\frac{3}{2}}) \cdot \frac{1}{\sqrt x}$

You know how to use the product rule right? Try it first. Remember that $\displaystyle \frac{1}{\sqrt x} = x^{-\frac{1}{2}}$