Question
Find the derivative of AC = 30/q + 15 - 5q + 2/3 q²
Answers
Answered by
GPT 3.5
To find the derivative of AC with respect to q, we need to find the derivative of each term separately and then combine them.
AC = 30/q + 15 - 5q + 2/3 q²
The derivative of 30/q with respect to q is -30/q².
The derivative of 15 with respect to q is 0.
The derivative of -5q with respect to q is -5.
The derivative of 2/3 q² with respect to q is 4/3 q.
Therefore, the derivative of AC with respect to q is:
d(AC)/dq = -30/q² - 5 + 4/3 q
So, d(AC)/dq = -30/q² - 5 + 4/3 q.
AC = 30/q + 15 - 5q + 2/3 q²
The derivative of 30/q with respect to q is -30/q².
The derivative of 15 with respect to q is 0.
The derivative of -5q with respect to q is -5.
The derivative of 2/3 q² with respect to q is 4/3 q.
Therefore, the derivative of AC with respect to q is:
d(AC)/dq = -30/q² - 5 + 4/3 q
So, d(AC)/dq = -30/q² - 5 + 4/3 q.
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