5. (a) Find the directional derivative of f(x, y) = √√x² − y² at P(5,3) in the direction of v = (1,-1). (b) Find the unit vector u in the direction of which ƒ has the maximum rate of change at (5,3). What is this maximum rate of change?

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A: We have to solve the problem

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A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

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Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

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Q: value of the dir function

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Q: find the directional derivative for z=2xy-3sqrt(xy) at point (1,1) in the direction of point (3,2).…

A: Directional derivative is same as rate of change in that direction