1. AP Calculus BC
September 12, 2016

2. Entry Task
What is f’(x)
𝑓 𝑥 =cos⁡(9 𝑥 2 )

3. hOMEWORK

4. Learning Targets
I can determine the derivative of functions using Implicit differentiation
I correctly solved problems involving the derivative of functions.

5. The Derivative
The derivative of f at x is given by 𝑓 ′ 𝑥 = lim ℎ →0 𝑓 𝑥+ℎ −𝑓 𝑥 ℎ provided that the limit exists.
The derivative of f at x is the slope of the tangent line through x.

6. Rules for Differentiation
You can use the definition of a limit to derive many basic rules for differentiation:
The Constant Rule
The Power Rule
The Constant Multiple Rule
The Sum and Difference Rules
The Product and Quotient Rules
Derivatives of Trigonometric Functions
Chain Rule

7. Implicit Differentiation
Functions can be defined in explicit form:
𝑦 = 3𝑥2 – 2𝑠𝑖𝑛𝑥
Or in implicit form:
𝑥2𝑦 + 𝑥𝑦 − 3𝑦2 = 4
We can use the Chain Rule to find the derivative of implicitly defined functions.

8. Find the derivative in terms of x
3 𝑦 2
𝑥+3𝑦
𝑦 3 + 𝑦 2 −4𝑦 − 𝑥 2 =4

9. Find the slope of the graph
3 𝑥 2 + 𝑦 =100𝑥𝑦 at point (3,1)

10. The Second Derivative Given 𝑥 2 + 𝑦 2 =25 find 𝑑 2 𝑦 𝑑 𝑥 2
Evaluate the first and second derivative at (-3,4)

11. Learning Targets
I can determine the derivative of functions using Implicit differentiation
I correctly solved problems involving the derivative of functions.

12. Assignment #8
§2.5 pp : 9, 13, 27, 31, 37, 47, 53, 57, 65