Another question about implicit differentiation.

[jaydnul]

Say you have x^2+y^2=100. why can't you just solve for y, so y=+- √(100-x^2) then use the chain rule to find the derivative. so y'= +- x/√(100-x^2). Then you can just deduce that y'= -x/y. What is the point of adding all the dy/dx in the equation? Seems like it just complicates it.

 

[SteamKing]

The point of implicit differentiation is that it avoids having to find x in terms of y before taking the derivative. In the example function you have chosen, y can be found in terms of x easily. There are functions where such is not the case. Implicit differentiation is the only technique which can be used in those cases.