Lesson 5: 3.5 Implicit Differentiation
Duration of Days: 3
Lesson Objective
Students will understand and apply differentiation to equations in which the dependent variable is not explicitly defined in terms of the independent variable. (The variables are defined implicitly in terms of each other.)
1. How to we find the derivative (dy/dx) when it is impossible to separate y from x and define y explicitly in terms of x?
2. How can we use implicit differentiation to find derivatives of inverse trigonometric functions?
- implicitly defined equations
- implicit differentiation
- inverse trigonometric functions
(Differentiation Rules)
Implicit Differentiation:
DOK levels 1-4
Derivative as a rate of change, such as velocity, etc.
- after having worked with many derivatives that only included x (the independent variable), it is somewhat strange to see derivatives that include both x and y expressions
- remembering derivatives for inverse trig functions can be tricky as they are all very similar
Homogeneous grouping and whole-class discussion
section assessment
Problems assigned from book