Homework SourseLet zlnx2y2 where xsquarootst and yst use the chain rule to
Let z=ln(x^2+y^2) where x=squaroot(st) and y=s+t. use the chain rule to express ?z/?s and ?z/?t in terms of s and t.
Solution
z= ln(x2+y2)
x= sqrt(st)
dx/ds= 1/(2*(st))
dx/dt=1/(2*(st))
y= (s+t)
dy/ds=t
dy/dt=s
z= ln(st+ (s+t)^2)
dz/ds= (2s+3t)/((s+t)^2 + st)
dz/dt= (3s+2t)/((s+t)^2 + st)
