q=(1000/p+1)^2 - 1
find q'
I will be happy to critique your thinking.
To find the derivative of the function q=(1000/p+1)^2 - 1, we can use the power rule and chain rule.
Step 1: Expand the expression q=(1000/p+1)^2 - 1
q = (1000/p + 1)(1000/p + 1) - 1
= (1000^2)/(p^2) + 2000/p + 1 - 1
= 1000000/(p^2) + 2000/p
Step 2: Differentiate q with respect to p
q' = d/dp(1000000/(p^2) + 2000/p)
Using the power rule and the chain rule,
q' = -1000000(2p^(-3))/p^2 - 2000(1/p^2)
= -2000000/p^3 - 2000/p^2
Therefore, the derivative of q is q' = -2000000/p^3 - 2000/p^2.