CHAPTER 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) / /

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

CHAPTER 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

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

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

CHAPTER 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)