q=(100/p+1)^2 - 1
what is q'?
use the chain rule:
q' = 2(100/p+1)(-100/(p^2))
i got
q' = 2(100/(p+1))(-100(p+1)^-2
=-2000/(p+1)^3
To find the derivative of q, q', you are correct in using the chain rule.
Let's break it down step by step:
1. Start by differentiating the outer function, which is (100/p + 1)^2.
Applying the power rule, you get 2(100/p + 1)^(2-1).
2. Now, differentiate the inner function, 100/p + 1.
The derivative of 100/p is -100/p^2, and the derivative of 1 is 0 since it is a constant.
3. Next, multiply the derivative of the outer function by the derivative of the inner function.
So, 2(100/p + 1)(-100/p^2).
Simplifying further, you can combine the two terms inside the parentheses:
q' = 2(-100/(p^2))(100/p + 1).
Finally, you can simplify this expression:
q' = -200(100/(p^2))(1/p + 1).
Adding the fractions, you get:
q' = -200(100+p)/(p^3).
Therefore, the derivative of q, q', is -200(100+p)/(p^3).