Let f(x, y) = y, and g(s, t) = [4s+3t, 2s+t]T. Find the partial derivative F of F(s, t) = f(g(s, t)) using the chain rule. of OF as

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 3

Let F(u, v) = eu+v, u = Use the Chain Rule to calculate the partial derivative. (Use symbolic notation and fractions where needed. Express the answer in terms of independent variables.) OF ду x² xº, v = 7xy. =

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).