Question

Implicit differentiation for xy^2+x^2y=7

Answer 1

Derivative Sum Rule\[(xy ^{2})\prime+(x ^{2}y)\prime = 7\prime\]
Product Rule\[(y ^{2}+x2yy \prime) + (2xy+x ^{2}y \prime)=0\]
Grouping y' terms\[y \prime(x ^{2}+2yx)=-2xy-y^2\]
can you do it from there?