If x3+3xy+2y3=17, then in terms of x and y, dxdy=
Differentiate both sides of the equation with respect to x.
x3+3xy+2y3=17
dxd(x3+3xy+2y3)=dxd(17)
Using the appropriate rules for each term,
power ruledxd(x3)+3product/chain ruledxd(xy)+2power/chain ruledxd(y3)=constant ruledxd(17)
3x2+3(x⋅dxdy+y⋅1)+2⋅3y2⋅dxdy=0
We can divide all terms by 3, then solve for dxdy:
x2+xdxdy+y+2y2dxdy=0
xdxdy+2y2dxdy=−x2−y
(x+2y2)dxdy=−(x2+y)
dxdy=−x+2y2x2+y