Mathematics 1 Deneme Sınavı Sorusu #1264166

For z = x²+xy, and x=u²-v and y=-uv, find the partial derivative ?z / ?v at u=2, v=-1.


-22

-12

0

7

9


Yanıt Açıklaması:

?z / ?v = (?z / ?x) . (?x / ?v)+ (?z / ?y) . (?y / ?v)

?z / ?v = (2x+y) . (-1) + (x) . (-u)

Hence, x=u²-v and y=-uv

?z / ?v = (2(u²-v)+(-uv)) . (-1) + (u²-v) . (-u)

By the way u=2, v=-1

?z / ?v = (2(5)+(2)) . (-1) + (5) . (-2)= -22

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