Implicit Differentiation: Find Slopes Without Solving for y

Implicit differentiation lets us differentiate an equation without first isolating $y$. We treat $y$ as a function of $x$, differentiate both sides, and apply the Chain Rule to every term involving $y$. 1

In this lesson, you will find $dy/dx$ for a circle, the folium , and a trigonometric product. You will also evaluate slopes, write tangent lines, interpret a zero denominator as a possible vertical tangent, and practice the four exam-credit steps: differentiate, collect, factor, and divide. 2