Math 1210 Quiz 4 February 7th, 2014

Math 1210
Quiz 4
February 7th, 2014
Answer the following two (2) questions. The value of every question is
indicated at the beginning of it. You may use scratch paper, but you can
only turn in this sheet. Please write your answer in the space provided. You
have 20 minutes.
1. (10 points) Use the chain rule to compute the derivatives of these functions:
2 x
(i) (7 points) f (x) = cos 1−x
2 x
(ii) (3 points) f (x) = cos4 1−x
(Note: this is just the 4th power of the function in
part (i), so most of the work is already done!)
2. (10 points) The equation
y 3 + 7y = x3
determines y as an implicit function y = f (x). Find y 0 = Dx (y) and y 00 = Dx2 (y) by
implicit differentiation.
(i) (7 points) y 0 =
(ii) (3 points) y 00 =
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