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: Given that hx=fx.gxh'x=f'x.gx+fx.g'xh'2=f'2.g2+f2.g'2h'2=4×3+2×3h'2=12+6h'2=18

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A: As per guideline we can solve maximum one question you can repost other question

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A: We can find the derivative using product rule in the below steps.

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A: Here we have to solve the differential equation.