Implicit differentiation for JEE

Formula

\[F(x,y)=0\Rightarrow \frac{dy}{dx}=-\frac{F_x}{F_y}\]

Variables: \(F_x=\partial F/\partial x\), \(F_y=\partial F/\partial y\).

Conditions: \(F_y\neq 0\) and relation defines \(y\) locally as differentiable function of \(x\).

Curves not given explicitly, tangent/normal questions.