00:01
So we have this revenue function r, and we want to find the marginal revenue function, m, which is just equal to the first derivative or r prime, the first derivative of our revenue function or r prime.
00:13
So we can say that m is equal to the derivative of 50 times x minus 0 .5, which i'm just going to denote as one -half times x squared.
00:27
And so we can split this derivative up whenever we have a derivative of one term plus or minus the derivative, or whenever we have the derivative of one term plus or minus another term, that's equal to the derivative of the first term plus or minus the derivative of the second term.
00:51
And so now what we can do is we can take out the constant 50 and the constant one -half, since whenever you have a constant multiplied by our variable, in this case, x, we can actually take that out of our derivative and then multiply it by the resulting derivative.
01:06
So this would be equal to 50 times the derivative of x minus one -half times the derivative of x squared.
01:21
And now we just need to find that, or now we just need to use the product rule, sorry, not the product rule, the power rule, to find the derivative of x and x squared...