2. CHAPTER 2 2.4 Continuity The Product and Quotient Rules Though the derivative of the sum of two functions is the the sum of their derivatives, an analogous statement is not true for products, nor for quotients. [ f(x)/ g(x)]’ = f’(x) /g’(x) [ f(x) g(x)]’ = f’(x) g’(x) / /

3. CHAPTER 2 2.4 Continuity The Product Rule If f and g are both differentiable, then [ f(x) g(x)]’ = f’(x) g(x) + f(x) g’(x)

4. CHAPTER 2 2.4 Continuity The Quotient Rule If f and g are both differentiable, then f’(x)g(x)–f(x) g’(x) [f(x)/g(x)]’ = ------------------------- [g(x)] 2

5. CHAPTER 2 2.4 Continuity Example Find the derivative of y = ( u 2 – u – 2 ) / ( u + 1 ).

6. CHAPTER 2 2.4 Continuity Example Find the derivatives of y = ( e x ) / ( x + e x ).

7. CHAPTER 2 2.4 Continuity Problem If f(3) = 4, g (3) = 2, f’(3) = 6 and g’(3) = 5, find the following numbers. a)( f + g)’(3) b) (f g)’(3) c) (f / g)’(3)