Use the Chain Rule to calculate the partial derivatives g(x, y) = sin(x² + y²), x=4u+3v, y = v — 3u ag ди Əg Əv = Express your answer in terms of the independent variables u, v
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- Use the Chain Rule to evaluate the partial derivative that the point (q, r) = (2, 2), where h(u, v) = ue", u = qª, v = qr². (Use symbolic notation and fractions where needed.) dh əq \(q.r) =Find the partial derivative of fy for the function * 3 f (æ,y) = (3x +y) 3r² (3x² + y²)² Option 2 6y (3x² + y²)² Option 4 3y (3x² + y²)² Option 1 2 6 (3x² + y²) ² Option 3Use the Chain Rule to find the indicated partial derivatives. P = √u2 + v2 + w², u = xey, v = yex, w = exy; ар ар when x = 0, y = 6 ах ду ӘР ?х ӘР ду || =
- Use the Chain Rule to evaluate the partial derivative at the point (q, r) = (2, 3), where h(u, v) = ue" , u = q°, v = qr³. (Use symbolic notation and fractions where needed.) ag lia)Use the Chain Rule to evaluate the partial derivative at the point (q, r) = (2, 3), where h(u, v) = ue" , u = q", v = qr'. (Use symbolic notation and fractions where needed.) ah dq l(g.r)Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test is inconclusive, so state. f(x,y) = -9х + 18ху - у + 81y; (- 3, - 3), (9,9) What is the nature of the function at (- 3, - 3)? O A. f(x,y) has neither a relative maximum nor a relative minimum at (-3, - 3). B. f(x,y) has a relative maximum at (- 3, - 3). C. f(x,y) has a relative minimum at (- 3, - 3). D. The second-derivative test is inconclusive at (- 3, – 3). What is the nature of the function at (9,9)? O A. f(x,y) has neither a relative maximum nor a relative minimum at (9,9). B. f(x,y) has a relative minimum at (9,9). O C. f(x,y) has a relative maximum at (9,9). O D. The second-derivative test is inconclusive at (9,9).
- Use the Chain Rule to evaluate the partial derivative h at the point (q, r) = (2, 3), where h(u, v) = ueº, u = qª, v = qr². да (Use symbolic notation and fractions where needed.) dh aq\(gr) =Find all the second-order partial derivatives of the function f(x,y) = 2x² +7y+ 6x?y. = 4 + 12y 12x дудх Enter your answer in the answer box and then click Check Answer.Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the independent F(u, v) = eU+v, ду u = x³, v= 4xy ƏF %3D
- Use the Chain Rule to evaluate the partial derivative (Use symbolic notation and fractions where needed.) dh dq \(q,r) = Əh at the point (q, r) = (1,2), where h(u, v) = ueº, u = qª, v = qr³. даFind the Partial Derivatives of the functions with respect to each variable 42 Mathematies Second Year Electrical & Flectronic Enginering Department Dr. Asheer Alaa Sabri 5) f(x,y)-Let -4x3 Oz Ax - Use partial derivatives to calculate Oz ду (2,5,-3) 3y3 + 5z3 - 2xyz +482=0. (2,5,-3) = = Oz дz and 3x ду at the point (2, 5, -3).