How do you use implicit differentiation to find y' for sin(xy) = 1?

1 Answer
Sep 12, 2014

By implicit differentiation, we can find
y'=1/{xcos(xy)}-y/x.

Let us work through it.

sin(xy)=1

by implicitly differentiating with respect to x,
Rightarrow cos(xy)cdot(1cdot y+x cdot y')=1

by dividing by cos(xy),
Rightarrow y+xy'=1/cos(xy)

by subtracting y,
Rightarrow xy'=1/cos(xy)-y

by dividing by x,
Rightarrow y'=1/{xcos(xy)}-y/x