q=2500+(600/r+2)-40p
Find dq/dp
q=3000-100z+(400/p+5)
Find dq/dp
Please help. Final tom and can't figure this out. I know it's simple.
Yes, they are simple. Show your work, I will critique it.
To find dq/dp, we need to differentiate the given expression q with respect to p.
For the first equation,
q = 2500 + (600/r + 2) - 40p
Let's break it down step by step:
1. Start by differentiating each term of the expression with respect to p:
- The differentiation of a constant term (2500) with respect to p is zero since it does not depend on p.
- For the term (600/r + 2), we need to apply the chain rule. The differentiation of 600/r with respect to p will be (600/r) * (-1/r) * dr/dp since r is a function of p. The differentiation of 2 (a constant term) with respect to p is zero.
2. Next, differentiate -40p with respect to p:
- For -40p, the differentiation of -40p with respect to p is -40 since p is the variable we are differentiating with respect to.
3. Combine the results from step 1 and 2:
The final expression for dq/dp is the sum of the differentiations we found in step 1 and 2.
Now let's move on to the second equation.
q = 3000 - 100z + (400/p + 5)
Following the same steps as above:
1. Differentiate each term with respect to p:
- The differentiation of 3000 (a constant term) with respect to p is zero.
- The differentiation of -100z (where z is a variable, but not p) with respect to p is also zero.
- For the term (400/p + 5), we need to apply the chain rule. The differentiation of 400/p with respect to p will be (400/p) * (-1/p) * dp/dp since p is a function of p. The differentiation of 5 (a constant term) with respect to p is zero.
2. Combine the results:
The final expression for dq/dp is the sum of the differentiations we found above.
Remember to double-check your work and apply the chain rule correctly if there are variables involved.