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Use the Chain Rule to find the indicated partial derivatives. и = = х2+ yz, x...

Question:

Use the Chain Rule to find the indicated partial derivatives. и = = х2+ yz, x = pr cos e, y = pr sin , 2 = p+r ди др au ar au
Use the Chain Rule to find the indicated partial derivatives. и = = х2+ yz, x = pr cos e, y = pr sin , 2 = p+r ди др au ar au де when p = 2, r= 1, = 0 ди др au ar ди де

Answers

Solution : Given that U = x3+yz , X = browse , y = brsîne , Z = +r = 4(37,2) =x+yz , x(br,e) = þrcose, y (er; e) = þrsing andSinee, y = prsine Then ay=psine 24 = $ sino/; ia he esmed ab 20 2p (10) (12) Sinee Z=b+p Then 2Z 1 a Z 1 = a Z 30 ao (13) (14de rette = 4.3 +0+0+0 → ne = 12 ap (Answer) From (17), weget 9 24. = 3x2bcose + z bsino + y From (2 we get 24 22 agar au zu tFrom (18), we get Ze ne au 20 au an ax 20 + - + Өe De ze = ne ax au 20 From (3), we get au au ay --3px?nsin 0 + z prcoso ay F

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