Lesson Plan: Implicit Differentiation Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use implicit differentiation to differentiate functions defined implicitly.
Objectives
Students will be able to
- use the chain rule in order to implicitly differentiate functions,
- know when it is simpler to use implicit differentiation even though it is possible to rearrange the relation and use explicit differentiation,
- find the slope of a curve at a given point using implicit differentiation,
- find the equation of a tangent to a curve at a given point using implicit differentiation,
- find higher-order derivatives of a function using implicit differentiation.
Prerequisites
Students should already be familiar with
- differentiating polynomial, trigonometric, and rational functions,
- the chain, product, and quotient rules of differentiation,
- higher-order derivatives,
- equations of tangents and normals to a curve.
Exclusions
Students will not cover
- differentiating exponential and logarithmic functions.
