00:01
Hi, in this question we have been given that average cost of producing q units of product given by 4500 e raised to the power q divided by 900 whole divided by q.
00:23
Then we need to find the marginal cost at q equal to 450 and 900.
00:28
So here marginal cost is given by derivative of the average cost function with respect to q.
00:39
So here if you differentiate, so 4500 is constant, we will take this out and then we need to differentiate e raised to the power q divided by 900 whole divided by q.
00:52
So here we will apply q divided by v differentiation rule.
00:57
So in this case we will take v constant and we will differentiate u and minus.
01:01
Now we will take u constant and differentiate v whole divided by v square.
01:07
So here also we will apply the same formula and then we will get here q multiplied by, if you differentiate this, so we will get 1 divided by 900 e raised to the power q divided by 900 minus here we will keep e raised to the power q divided by 900 constant and differentiate q.
01:28
So this will be 1 whole divided by q square.
01:32
So here if we take e raised to the power q divided by 900 common, so this will become 4500 e raised to the power q divided by 900 and this will become q minus 900 whole divided by 900 q square...