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Multivariable CalculusChallengePartial Derivatives & the Gradient

Partial Derivatives & the Gradient · Challenge problem

Let f(x,y)=xyf(x,y) = xy. At the point (4,3)(4,3) there are exactly two unit vectors u\mathbf{u} for which the directional derivative Duf(4,3)D_{\mathbf{u}}f(4,3) equals 44. Find the cosine of the angle between these two unit vectors.