Lesson 19: Partial Derivatives (worksheet)
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Worksheet for Lesson 19 (Section 15.3 and 15.5) Partial Derivatives Math 20 November 2, 2007 Find all first partial derivatives of the functions. 1. f (x, y) = 3x + 2xy 2 − 2y 4
2. w = sin α cos β
3. f (u, v) = arctan(u/v) (Remember that
d 1 arctan(x) = .) dx 1 + x2
1
4. u =
q
x21 + x22 + · · · + x2n
5. Find all the second derivatives of the functions in Problems 1 and 2.
00 00 6. Verify that f12 = f21 in Problem 3.
2
2. w = sin α cos β
3. f (u, v) = arctan(u/v) (Remember that
d 1 arctan(x) = .) dx 1 + x2
1
4. u =
q
x21 + x22 + · · · + x2n
5. Find all the second derivatives of the functions in Problems 1 and 2.
00 00 6. Verify that f12 = f21 in Problem 3.
2
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