1. Implicit Differentiation

2. Implicitly vs. Explicitly Defined Functions y is given explicitly as a function of x (y is solved in terms of x) y is given implicitly as a function of x (y is NOT solved in terms of x)

3. Some Graphs of Implicitly Defined Expressions

4. Graph of x-2xy=2

5. Graph of x 2 +y 2 =1

6. Graph of cos(x 2 )-sin(y 2 )=0

7. Implicit Differentiation When y is not given explicitly as a function of x, think of y as “locally” being a function of x. This approach is used to differentiate expressions where a term in the expression is considered implicitly as a function of another variable.

8. Graph of x-2xy=2 Find the equation of the tangent line at the point (2,0)

9. Graph of x 2 +y 2 =1 Find the equation of the tangent line at the point (√0.5, √0.5)