For z = x²+ylnx, and x=u³+v² and y=v, find the partial derivative ?z / ?v at u=1, v=0.

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

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

Hence, x=u³+v² and y=v

?z / ?v = (2(u³+v²)+(v/(u³+v²))) . (2v) + (ln(u³+v²)) . (1)

On substitution u=1, v=0

?z / ?v = (2(1)+(0)) . (0) + (0) . (1)= 0