I would like some assistance with the following integration and mutivariable calculus questions

4. Find the differential dw where w = 3x2 + 4-2:}; 2312. [2] 5. If T = f(x,y,z) and x,y and z are functions of s and t, write down a Chain Rule for 31" 3;- [4] 6. The equation F(x, y, w) = y3 + w3 + yxw.- 3y2 = 0, defines y as an implicit function of x and w. Find . [4] 7. Find the degree of homogeneity of the function f (x, y) = x3 - x2y + y3 and show that the function satisfies Euler's theorem. [8]8. Find the critical point for the function f(x, y) = xy - x - y + 3 and classify it as relative maximum, a relative minimum, or a saddle point. [10]4. Find I and 1 where f (x,y) = (x3y + xy2)5. [4] 5. The equation F(x, y, w) = y3x3w + x2w3 + yxw- 3y2 = 0, defines y as an implicit function of x and w. Find [2] 6. Letz = y?ex + xiny. Find the total differential dz. [4]6. Letz = y?ex + xIny. Find the total differential dz. [4] 7. State the degree of homogeneity of the function f (x, y) = 3 25 + 6 x2 + xy V2 [2]8. Find the critical point for the function f(x.y) = _x2 y2 + 6x + By 21 and classify it as a relative maximum, a relative minimum, or a saddle point. [11]