MATH 138 - Lecture 11 - Implicit Differentiation - Section 3.5

1. Implicit 3.5 Differentiation

2. 2
Circles
Figure 1

3. Example 1 – Finding a Tangent Line Implicitly
Implicit Solution:
(a) Differentiate both sides of the equation x2 + y2 = 25:
3

4. 4
Example 1 – Solution
Remembering that y is a function of x and using the Chain
Rule, we have
Thus
Now we solve this equation for dy/dx:
cont’d

5. 5
Example 1 – Solution
At the point (3, 4) we have x = 3 and y = 4, so
cont’d

6. 6
Implicit Differentiation
Differentiate term-by-term
Terms with a “y” (dependent variable) get a y’
Collect y’ terms on one side
Factor out y’
Solve for y’ by dividing

7. 7
Implicit Differentiation - Example