Calculus 3: Show Work

14.6Chainruleinseveralvariables:

1.

{1 point) Let f(x,y, z) : :2y' + 22 and a: = 32133, 3; : st\Let f(x, y) = 3x cos(y) y = 12r - 12s Use the Chain Rule to calculate the partial derivative of as at (r, s) = (2, 1). (Use symbolic notation and fractions where needed. Express the answer in terms of the independent variables.) of as (r, 8)=(2, 1) = help (fractions)Use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent variables. R(:, y] = [2: 43,09, 1 = 102, y = 1.1"" (Use symbolic notation and fractions where needed.) Let its, a) = i :l: = 3rt y = r91: Use the Chain Rule to calculate the partial derivative g . (Use symbolic notation and fractions where needed. Express the answer in terms of the independent variables.) 8f _ E : help (fractions) Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of @ (Figure 1). Suppose that Matthew runs with velocity V. (m/s) and Jessica with velocity Up (m/s). Let f(x, y) be the distance from Matthew to Jessica when Matthew is a meters from P and Jessica is y meters from P. P Va X B FIGURE 1 . Show that f(x, y) = vx2 +y2 - 2xy cos 0. . Assume that 0 = 7/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 16, y = 21, va = 5 m/s, and Vb = 4 m/s. dtCalculate the derivative % of 2153; + yaz + 2:23 2 6 using implicit differentiation. (Use symbolic notation and fractions where needed.) 3 _ _ a: _ help (fractions) Calculate the derivative using implicit differentiation: az ' xw + w2 + wz'+ 3yz =0Find the derivative of + ay (6) (7)+(6) (7) (6)(7)(6)(7) at (x, y, w) = (6, 6, 6) using implicit differentiation. (Use symbolic notation and fractions where needed.) help (fractions)Calculate the derivatives using implicit differentiation: and of (TU - V)? In(W - UV) = 1 at (T, U, V, W) = (6, 1, 3, 6) (6,1,3,6) aT = (6,1,3,6)