MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 13.5 Solutions Fa 2014

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

December 2, 2015: find dz/dt where z = x2y + xy2, x = t2, and y = t 2. Solution: by consulting theorem 13. 7 in the text book. Putting this together and plugging in for x and y, we nd dx dt dy dt. 2y (x y)2 3 cos t + 6 cos2 t 6 sin2 t (3 sin t cos t)2. 6 (3 sin t cos t)2: find the partial derivatives, fs and ft of the function f (x, y) = xy x2y2, where x = s + t and y = s t. Solution: in accordance with theorem 13. 8 dz dt. = (2xy + y2)2t + (x2 + 2xy)( 2t 3) = (2 + t 4)2t + (t4 + 2)( 2t 3) T: find dz/dt where z = x+y y = cos t. x y , x = 3 sin t, and. Let us calculate each part of this expression: By quotient rule treating y as a constant,