What is implicit differentiation...as in what would be the steps in solving it. I read my textbook but it seems very confusing.

Question

1) Differentiate both sides with respect to x
2) Realize that y is a function of x
3) Solve for y

Plus the d/dx notation made it even more confusing. Can someone please explain this to me simply? Thanks

Answer 1

http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/implicitdiffdirectory/ImplicitDiff.html

That is an excellent discussion.

Here is an example:
x^3 + xy^2 + x^2 y=14 find dy/dx

by implicit diff:
3x^2 dx/dx + y^2 dx/dx + 2yxdy/dx +2xydx/dx+x^2 dy/dx=0
butdx/dx is one, so

3x^2+y^2+2xy + dy/dx (2xy+x^2)=0

so dy/dx=-(3x^2+y^3 +2xy)/(2xy-x^2)