(This problem requires the use of calculus.) Consider a Cobb–Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function is: Y = K^(1/3).L^(1/3).H^(1/3)(a) Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor?(b) Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital?(c) What is the income share paid to labor? What is the income share paid to human capital? In the national income accounts of this economy, what share of total income do you think workers would appear to receive?