1. DIFFERENTIATION & INTEGRATION CHAPTER 4

2.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION

3.  Derivative of a Power Function Theorem 1  Derivative of a Constant Times a Function TECHNIQUES OF DIFFERENTIATION

5.  Derivative of Sum and Difference Rules

6.  Example :

7.  Derivative of a Product

8.  Example : Differentiate

9.  Derivative of Quotient

10.  Example : Differentiate

11. EXERCISE 1

12.  Derivative of Trigonometric Functions

13.  Example : Differentiate :

14.  Derivative of Exponential and Logarithmic Functions

15.  Example :

16.  The Chain Rule  Example :

17. EXERCISE 2

18.  Implicit Differentiation Implicit differentiation is the process of taking the derivative when y is defined implicitly or in y is a function of x.  Example :

19. EXERCISE 3

20.  A parametric derivative is a technique for finding derivative when both x and y variables depend on an independent third variable, t (time). PARAMETRIC DIFFERENTIATION

21. Example : Solve for if:

22.  Consider y =f(x) with point for function of a graph.  Tangent line – straight line that touches y = f(x).  Normal line – line that is perpendicular to tangent line.  Slope of tangent line,  Equation of the line tangent  Equation of normal line TANGENT AND NORMAL LINE

23.  Example : Given a curve equation at point (2,-1). a)Implicitly differentiate the equation.

24. b) Find the equation of the line tangent of the curve. Step 1 : Find the slope of tangent, m. Step 2 : Find the equation using

25. c) Find the equation of the normal line of the curve.

26. 1.If, find the equation of the tangent line at (-1,4). 2.If, find the slope of the tangent line to the curve where. Find the equation of the line tangent to the curve where EXERCISE 4