### Definition Differentiating both sides of an [[Implicit Equation]] ## Notes A curve that may have no explicit form, can be described by an equation. If both sides of that equation are differentiable, then they should have the same derivative. In equations of $x$ and $y$, typically the derivative is taken with respect to $x$ in hopes of finding $dy/dx$ even if it does not turn out to be an [[Explicit Function]] of only $x$. This means a valid point $(x,y)$ from the [[Implicit Equation]] must be substituted into resulting equation to find $dy/dx$ at a point on the curve This technique works for [[Higher order derivatives]]