1.
f(x,y)=x^2+2xy^2+2y^3
x=r+2s
y=3r+2s
df/dr= (df/dx)(dx/dr)+(df/dy)(dy/dr)
df/ds=(df/dx)(dx/ds)+(df/dy)(dy/ds)
dx/dr=1
dy/dr=3
dx/ds=2
dy/ds=2
df/dx=2x+2y^2
df/dy=6y^2+4xy
df/dr=(2x+2y^2)(1)+(6y^2+4xy)(3)
df/ds=(2x+2y^2)(2)+(6y^2+4xy)(2)


2.
x^2+y^3+z^2=5xyz+1
x^2+y^3+z^2-5xyz-1
df/dx=2x-5yz
df/dr= 3y^2-5xz