1. Calculus 2.1: Differentiation Formulas A. Derivative of a Constant: B. The Power Rule: C. Constant Multiple Rule:

2. D. Sum Rule: E. Difference Rule:

3. F. Product Rule: Ex 1: Find f ‘(x):

4. G. Quotient Rule Ex 2: Find y’

5. A. Higher Derivatives 1. Second Derivative: f’’ = (f’)’ (if f’ is differentiable) 2. Third Derivative: f’’’ = (f’’)’ (if f’’ is differentiable) Note: “y super n” means the nth derivative Calculus 2.2: Differentiation Problems

6. B. Examples 1. Find the equation of a tangent line at the point (1, ½) to the curve: 2. Find the points on the curve y = x 4 – 6x 2 + 4 where the tangent line is horizontal 3. At what points on the hyperbola xy = 12 is the tangent line parallel to 3x + y = 0? 4. If h(x) = xg(x) and it is known that g(3) = 5 and g‘(3) = 2, find h‘(3) 5. #37 p.124

7. Calculus 2.3: More Rates of Change A. Average Rate of Change of y with respect to x: B. Instantaneous Rate of Change: (derivative)

8. C. Applications 1. Linear Motion: a) velocity – the derivative of the position function s = f(t) b) speed – the absolute value of velocity c) acceleration – the derivative of the velocity with respect to time d) jerk – the derivative of acceleration

9. 2. Economics: a. marginal cost – the rate of change of cost with respect to level of production b. marginal revenue – the derivative of the revenue function

10. Calculus 2.4: Derivatives of Trigonometric Functions A. Derivatives of Trig Functions: (Memorize!!)

11. Graphing Sin/Cos Functions Graphing Sin/Cos Functions

12. Graphing Cos/-Sin Functions Graphing Cos/-Sin Functions

13. Calculus 2.5: The Chain Rule A. The Chain Rule: If f and g are both differentiable and F = f o g, then F is differentiable and F’ = f ‘(g(x))g‘(x) Ex 1:

14. B. Power Rule Combined with Chain Rule or

15. C. The Chain Rule (Trigonometric Functions) Find tangent line

16. Calculus 2.6: Implicit Differentiation A. Method of Implicit Differentiation: 1. Differentiate both sides of the equation with respect to x 2. Solve the resulting equation for B. Examples—find y’

17. B. Finding 1. Use implicit differentiation to find 2. Differentiate 3. Substitute the expression for 4. Simplify

18. C. Implicit Differentiation with Trigonometric Functions 1. sin(x+y) = y 2 cos x 2. tan(x/y) = x + y 3. 4 cos x sin y = 1 4. 2y = x 2 + sin y

19. Calculus Unit 2 Test Grademaster #1-30 (Name, Date, Subject, Period, Test Copy #) Grademaster #1-30 (Name, Date, Subject, Period, Test Copy #) Do Not Write on Test! Show All Work on Scratch Paper! Do Not Write on Test! Show All Work on Scratch Paper! Label BONUS QUESTIONS Clearly on Notebook Paper. (If you have time) Label BONUS QUESTIONS Clearly on Notebook Paper. (If you have time) Find Something QUIET To Do When Finished! Find Something QUIET To Do When Finished!