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2 If w =exp(x2y) and x = sin(11t) and y = 21cos(-33t), find δw/δt in two...

  1. 2 If w =exp(x2y) and x = sin(11t) and y = 21cos(-33t), find δw/δt in two ways, once by plugging in, and once by the chain rule.

3. Show why it is true that, if f(x, y) = 0 implicitly defines y as a function of x, we can compute the derivative dy/dx as the negative of the quotient of δf/δx and δf/δy.

4. Find the directional derivative of the function f(x,y) = (x+1)4 cos(-5y) at the point (0,1) in the direction from the point (3,0) toward the point (6,6).

BONUS: In what direction does the function in #4 have the maximal decrease at the point (3, 0)?

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