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- A household of two people has a home environment of quality u(x, y). if the younger person contributes x hours daily to household chores and the older person contributes y hours daily.a) How many first order partial derivatives does the function u have? What are they? b) Choose one of these and explain in words what it describes,in terms of home environment and hours spent on chores.c) What is the likely sign of the partial derivative you chose?Explain why.d) If the household expects guests, they would like to present them with a home environment of quality 10 during their stay. Relatethis desire to the concept of a level curve. Do you expect the level curve to be increasing or decreasing, and why?find the first partial derivatives of the given function. complete solution z= 3x2y - y3 + 4x - 73) Find all of the first-order partial derivatives of the function:g (x, y, z) = 10x2ln(y) + xyz3 Thank you for helping. I wanted to double check my answers before turning this in.
- let f(x, y) = 3xy^2 + y * ln(2x - 1) + 2x/ya) Find both first-order partial derivatives of f.b) Find all four second-order partial derivatives of f.c) State the domain and the range of f(x, y) Thank you, I am getting confused going from the four second order partial derivatives to the domain and range.Find the first partial derivatives of the function. w = 4zexyzYou are given the production function Q(K,L) = 500 K1/4 L3/4 where K represents capital and L represents labour. Evaluate its first order partial derivatives when K = 1296 and L = 81, interpret the value computed above for any one of the first order partial derivatives and estimate the change in production level Q which results from an increase of 3 units in K and a decrease of 2 units in L.
- Find all the second-order partial derivatives of the following function. 2 Parts remainingAssume that g(x, y, z) is a function of three variables withpartial derivatives of every order. Assume also the orderin which the partial derivatives are taken is significant.(a) How many different second-order partial derivativesdoes g have?(b) How many different third-order partial derivativesdoes g have?(c) How many different nth-order partial derivativesdoes g have?A man-made lake is going to be stocked with two types of fish. Let ? represent the number of bass, and let ? represent the number of catfish. The average weight of a bass is given by ?(?,?)=8−0.01?1/2 −0.05?, and the average weight of a catfish is given by ?(?,?)=20−0.01?−0.2?1/3. Find both partial derivatives of both functions when (?,?)=(100,125), and explain what they represent in words.
- Given the attatched function F, find all of the second partial derivatives. (Hint: you can solve the partial derivatives component by component)Find the first partial derivatives of the function. f(x, y) = x/(7+x) x 7 + yFind the second-order partial derivatives of the function. Show that the mixed partial derivatives fxy and fyx are equal. f(x, y) = ln(4 + x2y2) fxx=2^y^2(4−x^2y^2)/(x^2y^2+4)^2 fyy=2x^2(4-x^2y^2)/(x^2y^2+4)^2 fxy= ? fyx= ? I understood how to get the first two answers but after that everything I tried was wrong.