3. [20 points] Given function z=xsin(y/x). Find the following. (a) The gradient vector ∇z. (b) The directional derivativ
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3. [20 points] Given function z=xsin(y/x). Find the following. (a) The gradient vector ∇z. (b) The directional derivativ
3. [20 points] Given function z=xsin(y/x). Find the following. (a) The gradient vector ∇z. (b) The directional derivative of z at (1,π/2) along direction v=i−j. (c) Verify that the mixed partial derivatives zxy and zyx are equal. (d) Express ∂t∂z if x=en+t,y=en−t by the chain rule. Do NOT simplify.
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