# UT M 408C - HW 14.5-solutions-1 (4 pages)

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## HW 14.5-solutions-1

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- Pages:
- 4
- School:
- University of Texas at Austin
- Course:
- M 408c - Differential and Integral Calculus

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lewis scl876 HW 14 5 radin 55315 This print out should have 8 questions Multiple choice questions may continue on the next column or page find all choices before answering 10 0 points dw Use the Chain Rule to find when dt 1 002 10 0 points Use the Chain Rule to find 001 z when t x y z and y z w xe x 5set y 3 se t and x t2 y 4 t z 4 t dw x 4xy y z 1 e t dt z z dw x 4xy y z 2 e t dt z z dw x xy 3 2t 2 ey z dt z z x xy y z dw e 2t 4 dt z z dw x 4xy 5 t 2 ey z dt z z dw x xy 6 2t 2 ey z correct dt z z Explanation By the Chain Rule for Partial Differentiation dw w dx w dy w dz dt x dt y dt z dt When z syet xs 1 t yet syet xs z 2 t y 2 et 3 5sye2t xs z correct t y 2 et 4 z 5sye2t xs t yet 5 5syet xs z t y 2 et 6 sye2t xs z t yet Explanation By the Chain Rule for Partial Differentiation z z x z y t x t y t But w xey z 1 z x y x 5set t while and x t2 y 4 t z 4 t therefore x xy dw 2tey z ey z 2 ey z dt z z Consequently x xy y z dw 2t 2 e dt z z z x 2 y y y se t t Consequently 5sye2t xs z t y 2 et lewis scl876 HW 14 5 radin 55315 keywords 003 10 0 points u Use the Chain Rule to find for p u 2 3t 2 z x 2 2 y z p keywords x y y z 004 10 0 points F when z z y F to find for y y z 0 Use the equation x p 5r 3t y p 5r 3t xe8y yz ze5x and z p 5r 3t 1 z e5x y y z 8xe8y 1 u 3t 2 correct p p 2 8e8y y z y z e5x 2 3 u 2 p p 3 z 8xe8y z y y 5e5x 3 3t2 u 3 p p 4 8xe8y z z correct y y e5x 4 u 3t 2 p p 5 3 u 2 p p 8e8y y z 5 y z 5e5x Explanation Explanation By the Chain Rule 005 u x u y u z u p x p y p z p But u 1 x y z x 1 p 10 0 points The temperature at a point x y in the plane is T x y C If a bug crawls on the plane so that its position in the plane after t minutes

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