Additional Resources
OpenStax Online Textbook
How to Read a Math Textbook
Additional Instructional Resources
Implicit Differentiation- DS5
Objectives
- Find the derivative of a complicated function by using implicit differentiation.
- Use implicit differentiation to determine the equation of a tangent line.
Summary
In an equation involving and where portions of the graph can be defined by explicit functions of we say that is an implicit function of A good example of such a curve is the unit circle.
We use implicit differentiation to differentiate an implicitly defined function. We differentiate both sides of the equation with respect to treating as a function of by applying the chain rule. If possible, we subsequently solve for using algebra.
While may now involve both the variables and still gives the slope of the tangent line to the curve. It may be used to decide where the tangent line is horizontal or vertical ( is undefined), or to find the equation of the tangent line at a particular point on the curve.