EC4004 Economics Quantitatively Treated :Diffrentiation Assignment

Find the first derivatives, dx /dy of:

1. y = -3x-5
2. y=x^4/5
3. y = 4x^1/6 + 3
4. y =3x^-5 +ax^ 2
5. y = ax^b+1 + ax^2
6. y=3/x^2/3
7. y=3/x^-2/3
8. What is the slope of the following function y =x^3 -2x^2 +4 at
   1. x = 2
   2. x = -4
   3. x = 1/3
9. Find the price elasticity of demand for each of the following demand functions when P = 4
   1. Q =98-P^2/2
   2. Q =14P^-2
10. Find the price elasticity of supply for each of the following supply functions when P = 3
    1. Q =-2 +5P
    2. Q =-12 +4P +P^2
11. A firm has a demand function: P = 20 Q and a total cost function: TC(Q) =1/3Q^3-6Q^2+29Q+15 Find:
    1. The marginal revenue and marginal cost functions.
    2. By setting marginal revenue equal to marginal cost find the profit maximizing level of output.