Question: Consider the functions z = 6 e x l n ( u c o s v ) and y = u s i n v

Consider the functionsz=6exln(ucosv) and y=usinv.

a)Expressuz andvz as function of u and v both by using the Chain Rule and by expressing z directly in tems of u and v before differentiating

b) Evaluateuz andvz at (u,v)=(5,4)

(a) Find each partial derivative needed to use the Chain Rule to finduz

xz= yz=

ux= uy=

Express z directly in terms of u and v.

z=

Using either method,uz=

Find each partial derivative needed to use the Chain Rule to findvz

xz= vx=

yz= vy=

Using either method,vz=

b)uz(5,4)=

vz(5,4)=

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