derivatives with a twist

**foxracing** · January 21st 2009, 06:15 PM

Hey, just found this forum and wanted to give a quick thanks beforehand.

I took calc a year ago and did ok, but now i need to know some calc for an econ class im in.

Here's a sample question...
Q=10L^.75 K^.25
In my calc class we just had to do the math, and i would multiply the exponent to the coefficient and minus the exponent by 1. I'm 99.9% this is correct.

But my econ teacher wants us to caclucate to sets:
a. calculate derivative Q/derivative L
b. calculate derivative Q/derivative K

I'm lost on that part. Thanks

**mollymcf2009** · January 21st 2009, 06:45 PM

Is the sample equation you posted the equation you are supposed to use to determine the two sets for a value? You will need to use the product rule to get the derivative for the sample problem because you are multiplying two variables and the quotient rule for the Q/K problems. Can you be more specific about what you are solving for?

**foxracing** · January 21st 2009, 06:55 PM

Sorry if i wasnt too clear.
Heres the exact problem:

Consider the following function Q= 10L^.75 K^.25
a. Calculate derivative Q/derivative L
b. Calculate derivative Q/derivative k

I figure if i can figure out a or b, i can do the other one.

**mollymcf2009** · January 21st 2009, 07:22 PM

Product rule:
Q = lk
Q' = l'k +lk'

So,

Q = $10l^{.75}k^{.25}$

Q' = $7.5l^{-.25}k^{.25} + 10l^{.75}.25k^{-.75}$

I laid out the product rule for you. See if you can finish it and then go from there. Come back if you get stuck!!

**mr fantastic** · January 21st 2009, 09:27 PM

Originally Posted by foxracing

Sorry if i wasnt too clear.
Heres the exact problem:

Consider the following function Q= 10L^.75 K^.25
a. Calculate derivative Q/derivative L
b. Calculate derivative Q/derivative k

I figure if i can figure out a or b, i can do the other one.

The question as you've posted it requires the idea of a partial derivative. have you learned about this?

To get $\frac{\partial Q}{\partial L}$ , you treat K as if it were a constant. Then:

$\frac{\partial Q}{\partial L} = 0.75 L^{-0.25} K^{0.25}$ .

The other is done in a similar way and is left for you to attempt.

**mr fantastic** · January 21st 2009, 09:29 PM

Originally Posted by mollymcf2009

Product rule:
Q = lk
Q' = l'k +lk'

So,

Q = $10l^{.75}k^{.25}$

Q' = $7.5l^{-.25}k^{.25} + 10l^{.75}.25k^{-.75}$

I laid out the product rule for you. See if you can finish it and then go from there. Come back if you get stuck!!

The problem as posted requires the idea of a partial derivative. See my post above. So gettting a total derivative (with respect to x ....?) is not correct.

**Mush** · January 21st 2009, 09:34 PM

Originally Posted by foxracing

Hey, just found this forum and wanted to give a quick thanks beforehand.

I took calc a year ago and did ok, but now i need to know some calc for an econ class im in.

Here's a sample question...
Q=10L^.75 K^.25
In my calc class we just had to do the math, and i would multiply the exponent to the coefficient and minus the exponent by 1. I'm 99.9% this is correct.

But my econ teacher wants us to caclucate to sets:
a. calculate derivative Q/derivative L
b. calculate derivative Q/derivative K

I'm lost on that part. Thanks

$\frac{dQ}{dK}$ means you differentiate the equation with respect to variable K, and present that all other variables are constants! $\frac{dQ}{dL}$ means the same thing, except you differentiate with respect to L, and present that K is a constant!

SO!

$\frac{dQ}{dK} = \frac{d}{dQ} 10L^{\frac{3}{4}} K^{\frac{1}{4}}$

$= 10L^{\frac{3}{4}}\frac{d}{dQ} (K^{\frac{1}{4}})$

$= 10L^{\frac{3}{4}} ( \frac{1}{4}K^{\frac{-3}{4}})$

$= \frac{10}{4}L^{\frac{3}{4}} K^{\frac{-3}{4}}$

$= \frac{5}{2}L^{\frac{3}{4}} K^{\frac{-3}{4}}$

$\frac{dQ}{dL} = \frac{d}{dL} 10L^{\frac{3}{4}} K^{\frac{1}{4}}$

$= K^{\frac{1}{4}} \frac{d}{dQ}(10L^{\frac{3}{4}})$

$= K^{\frac{1}{4}} (\frac{3}{4}10L^{\frac{-1}{4}})$

$= K^{\frac{1}{4}} (\frac{30}{4}L^{\frac{-1}{4}})$

$= K^{\frac{1}{4}} (\frac{15}{2}L^{\frac{-1}{4}})$

$= \frac{15}{2}K^{\frac{1}{4}} L^{\frac{-1}{4}}$

Thread: derivatives with a twist

LinkBack

Thread Tools

Display

derivatives with a twist

Similar Math Help Forum Discussions

New Twist to an old puzzle

Interest compounding with a twist

ratios with a twist

Triangle problem with a twist!!!

min/max with a twist

Search Tags