Suppose thatF (x, y) = g(u(x, y), v(x, y))with u(x, y) = x2 and v(x, y) = h(x, y) − x. Furthermore suppose thath(1, 1) = 2, hx(1, 1) = 3, hy(1, 1) = −2, g(1, 1) = 6, gu(1, 1) = −4 andgv(1, 1) = 5. Determine the partial derivatives Fx(1, 1) and Fy(1, 1).

For the function of two variables f (x, y) = 4x3 + 6x2y2 − 7xy3 − 8y4 find the second order partial derivatives fxx, fyy and fxy (note that fxy should equal fyx).

Given the function f(x, y) = x2y4 − cos 2xy, find the partial derivatives

How many independent variables are there in a general utility function of the form U=h(x,y)Question 3Select one:a.3b.4c.2d.1

Consider the vectors u = (−3/5, −4/5), v = (4/√20, 2/√20), w = (−3/√11, 2/√11). For a functionf (x, y), the directional derivatives of f at some point (a, b) with respect to u and v are given by Duf (a, b) =14/5 and Dvf (a, b) = −22/√20. Determine the value of Dwf (a, b)

Compute all the first and second partial derivatives of the function. We assume that y>0𝑦>0 .f(x,y)=xy−3x−ln(y6) .