Rate of change of demand

sktsasus

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Rate of change - Implicit differentiation

"A price p (in dollars) and demand x for a product are related by


(2x^2)-2xp+50p^2 = 20600.


If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand."


I was a little confused on how to proceed with this question. Am I supposed to use implicit differentiation (with the x serving the same purpose as a y) and then find the derivative of x?

This is the implicit differentiation I tried:

4x(dx/dp)-2(dx/dp)+100p = 0

4x(dx/dp)-2(dx/dp) = -100p

dx/dp(4x-2) = -100p

dx/dp = -100p/4x-2

I believe this is the derivative I am looking for (though not entirely sure) but I am not sure what values of p and x to input, as I am supposed to get a numerical final answer.

Any help?
 
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"A price p (in dollars) and demand x for a product are related by


(2x^2)-2xp+50p^2 = 20600.


If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand."


I was a little confused on how to proceed with this question. Am I supposed to use implicit differentiation (with the x serving the same purpose as a y) and then find the derivative of x?

This is the implicit differentiation I tried:

4x(dx/dp)-2(dx/dp)+100p = 0

4x(dx/dp)-2(dx/dp) = -100p

dx/dp(4x-2) = -100p

dx/dp = -100p/4x-2

I believe this is the derivative I am looking for (though not entirely sure) but I am not sure what values of p and x to input, as I am supposed to get a numerical final answer.

Any help?

If x = f(p), \(\displaystyle \dfrac{d}{dp}2xp = 2\left(x + p\cdot\dfrac{dx}{dp} \right)\)

You may have overlooked your Product Rule.


The problem statement tells you dp = 2 and p = 20
 
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