MATH 205 Quiz: MATH 205 Louisville Quiz 4 150220 Solution
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Quiz #4 solutions: (7 points) given the equation ey = x + xy, determine dy dx by implicit di erentiation. At this point the calculus is complete and all we need to do is algebraically isolate the dy dx: dy ey = 1 + y + x dy dx ey dy dx dx x (ey. X) dy dx dy dx dy dx. X: (6 points) find the derivative with respect to x of the expression x 1 + ex. This is on the most straightforward level a product of two things, so we will use the product rule. However, one of those two factors, 1 + ex, is a composition so we will nd ourselves using the chain rule. With that game plan in mind, we proceed to perform the di erentiation: d dx (x 1 + ex) = ( d dx: 1 + ex + x d dx. U for u = 1 + ex du du d dx.
