6. [-/8 Points] DETAILS SCALCET8 14.5.052. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = 5r cos(0) and y = 5r sin(0), find the following (a) dz ar az az ar ax ay Oz (b) ae az az ae ax ay azz (c) ar de azz az + ar de or + azz azz ax ay2 2x 2 azz ay ax 7. [-/1 Points] DETAILS SCALCET8 14.6.004. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the directional derivative of f at the given point in the direction indicated by the angle 0. f( x, y) = xy3 - x2, (1, 2), 0 =1/3 Duf( 1, 2) = 8. [-/1 Points] DETAILS SCALCET8 14.6.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the directional derivative of f at the given point in the direction indicated by the angle 0. f( x, y) = y cos(xy), (0, 1), 0 = 1/4 Duf (0, 1 ) = 9. [-/3 Points] DETAILS SCALCET8 14.6.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. f ( x, y, z) = x2yz - xyz3, P( 2, - 1, 1), u = (0, 5, -) (a) Find the gradient of f. Vf ( x , y , z ) = (b) Evaluate the gradient at the point P. Vf( 2, - 1, 1 ) = (c) Find the rate of change of f at P in the direction of the vector u. Duf ( 2 , - 1, 1) = Need Help? Watch It