Compute the derivative of f(x, y) = x2y + x with respect to t where: ac ( t) = 3+5 and y(t) = et Your answer should have only the variable t in it. df Answer: dt Write vu for yl Write v*u for v . u (* is required) Write v*(u+w) for v(u + w) (parenthesis and * are required) Write e for e (parenthesis are required)Compute the partial derivative of x, y) = 11:6 l 5\" with respect to 'r' where: 1:0", 3] : s (305(5)?) and Mr", 3] = 53 -l 1' Your answer should have only the variables a" and s in it. 33' Answer entry help: Be careful with brackets, check how the system interprets your answer. Write vAu fer 1;\" Write v*u for u - u (* is required] ' it Write v*(u+w] for u(u l w} (parenthesis and are required) ' h Write E (\"Jr\") for e (parenthesis are required] Write cps(theta) for (:05 El {parenthesis are required) Let f(m)yiz): m Parta. If Vf[l,0,=(a,b,c] then a b : (3: DUB Part b. If M denote the maximal rate of change of f at the point (1, 0, x/Q) then AME Part c. if the unit vector u = (11,3, C) denote the direction in which maximal rate of change of f it occurs, then t. EDD B: 0': Answer entry help: 1. No blank spaces are allowed in the answer fields 2. If your answer a = Z please write only Z in the answer box. Note that a: = is already written. Thus, ifyou put a. = Z in the answer box, the system will read this as a. = a = Z and will treat as a wrong answer. 3. Write v": I)'2 Write v*z for v - z (multiplication of v by 2) Write ln(z) for ].u z (parenthesis are required) Write sqrt(z) for (parenthesis are required) Write sin(z) for sinz (parenthesis are required] Write pi for 7r Let flan/J) = as (mm + 2. Part a. If VO, 52, U) : (a,b,c) then _ _ _ _ _ _ _ a (4.2.4). Part b. The directional derivative of f at (0, 62, 0) in the direction of vector u : IS 6 wa Answer entry help: 1. N0 blank spaces are allowed in the answer fields 2. If your answer a : Z please write only Z in the answer box. Note that a : is already written. Thus, ifyou put a : Z in the answer box, the system will read this as a : a : Z and will treat as a wrong answer. 3. Write VAZ Us Write V'z for v . z (multiplication of v by 2) Write ln(z) for in z (parenthesis are required) Write sqrt(z) for J; (parenthesis are required) Write sin(z] for sin: (parenthesis are required] Write pi for 1r 6 __ y at the point (1, 2,4) is The equation of the tangent plane to the graph of x, y] = 1 1' z = : Answer entry help: Note 2 = is already written, if you write it again the system will read 2 = z =. . . and treat it as a mistake. I will NOT add points for such a mistake. Write X\")! for my Write x*y for :v - y (* is required) Write cos(theta) for cost? (parenthesis are required) Write sqrt(z) for (parenthesis are required) Write cos(sqrt(z)) for cosh/E) Write cos(sqrt(z))*sqrt(\\pi/2) for Cos('/E)\\/1r/2 Write pi for 11' Write e for e Let z = Ax + By + D be the tangent plane to the surface given by In x 2 = y at the point (1/9, 1, - In 9). Then A = B D Answer entry help: Write u^v for u" Write u*v for u . v (* is required) Write e for e Write In(u) for In u (parenthesis are required)