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Material Type: Quiz; Professor: Ellermeyer; Class: Calculus III; University: Kennesaw State University; Term: Spring 2006;
Typology: Quizzes
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MATH 2203 ñQuiz 4 SolutionFebruary 24, 2006
NAME________________________________ For the function f (x; y) =^3 yx 2 + y yex^ sin (xy) , compute the partial derivatives fx, fy, fyx, and fxy. Solution: It is convenient to write the formula for f as f (x; y) = 3xy ^2 + y yex^ sin (xy). Using basic di§erentiation rules, we obtain fx = 3y ^2 yex^ y cos (xy) fy = 6 xy ^3 + 1 ex^ x cos (xy) fyx = 6 y ^3 ex^ + xy sin (xy) cos (xy) and f xy =^ ^6 y ^3 ^ ex^ +^ xy^ sin (xy)^ ^ cos (xy)^.
