Given the cobbdouglass production function Q K12 L12 Find t

Given the cobb-douglass production function Q = K^1/2 L^1/2 Find the differential dQ and d^2Q

Solution

Given that

Q = K^1/2L^1/2

dQ = d/dK(K^1/2) L^1/2 + K^1/2.d/dL( L^1/2 ) [ since, (f.g)\' = f\'.g + f.g\' ]

dQ = (1/2)K^(1/2)-1.L^1/2 + K^1/2.(1/2)L^(1/2)-1 [ Since , d/dx(xⁿ) = nx^n-1 ]

   dQ = (1/2)K^-1/2L^1/2 + (1/2)K^1/2L^-1/2