How do you get the derivative of :?

Question

This equation:

25,000 + 150 + 3Q
---------------
Q

The answer is:

-25,000 + 3
_______

Q ^2


But how do you get there?

Answer 1

Use the quotient rule
The derivative is
[(Q)(25000 +150 + 3Q)' - (25000 + 150 + 3Q)(Q)'] / (Q)^2
= [(Q)(3) - (25000 + 150 + 3Q)(1)] / Q^2
= [3Q - 25000 - 150 - 3Q] / Q^2
= [-25000 - 150]/ Q^2
= -25150/Q^2
If you want (and I would recommend this), then you can combine 25000 and 150 to get 25150.