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(a) Find an equation of the plane tangent to the surface xy ln x − y^2...

(a) Find an equation of the plane tangent to the surface xy ln x − y^2 + z^2 + 5 = 0 at the point (1, −3, 2)

(b) Find the directional derivative of f(x, y, z) = xy ln x − y^2 + z^2 + 5 at the point (1, −3, 2) in the direction of the vector < 1, 0, −1 >. (Hint: Use the results of partial derivatives from part(a))

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