Let z(x,y)=e^(3xy), x(p,q)=p/q and y(p,q)=q/p are functions. Use multivariable chain rule of partial derivatives to find (i) (delz)/(delp) (ii) (delz)/(delq).

Anish Buchanan 2021-01-06 Answered
Let z(x,y)=e3xy,x(p,q)=pqandy(p,q)=qp are functions. Use multivariable chain rule of partial derivatives to find
(i) zp
(ii) zq.
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Expert Answer

SoosteethicU
Answered 2021-01-07 Author has 102 answers

(i) zp=zxxp+zyyp (1)
⇒∵zx=e3xy3yzx=3ye3xy
zy=e3xy3xzy=3xe3xy
xp=1qandxq=9q2
yp=1p2andyp=1p
Using these values equation (1) becomes:
zp=3ye3xy1q+3xe3xy(qp2)
zp=3ye3xyq(3xqe3xyp2)
zp=(3e3xyqp2(p2yxq2))
(ii) zq=zxxq+zyyq
zq=3ye3xy(pq2)+3xe3xy(1p)
zq=(3ype3yxq2+3xpe3xy)
zq=(3e3xypq2(xq2yp2))

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