implicit differentiation

Differentiating both sides of an equation that isn't already solved for $y$ , treating $y$ as a function of $x$ .

Implicit differentiation applies $\dfrac{d}{dx}$ to both sides of an equation relating $x$ and $y$ , using the chain rule on every $y$ -term (since $y$ is a function of $x$ ), then solves the resulting equation for $\dfrac{dy}{dx}$ .

Examples

For $x^2+y^2=25$ : differentiating gives $2x+2y\,y''=0$ , so $y''=-x/y$ .