A dynamic property f(x, y) in a system can be described as below. With the consideration...

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A dynamic property f(x, y) in a system can be described as below. With the consideration of chain's rule answer (a) and (b): 2. f(x, y) = sin(x) y df dt a) Obtain the rate of change of property f(x,y) with respect to time (i.e. by using the concept of total derivative and chain's rule: use u= & v= for the velocities along x and y directions in the derivations. (10 point) dy dx dt dt b) Obtain the gradient vector of function (x, y) at point . 1 (i.e. 4 Vf(x, y)). (5 point) A dynamic property f(x, y) in a system can be described as below. With the consideration of chain's rule answer (a) and (b): 2. f(x, y) = sin(x) y df dt a) Obtain the rate of change of property f(x,y) with respect to time (i.e. by using the concept of total derivative and chain's rule: use u= & v= for the velocities along x and y directions in the derivations. (10 point) dy dx dt dt b) Obtain the gradient vector of function (x, y) at point . 1 (i.e. 4 Vf(x, y)). (5 point)