Since the derivative of a sum or difference of functions is simply the sum or difference of their individual derivatives, you might assume that the derivative of a product of functions is the product of their individual derivatives. This is not true. Eg.1: Let p(x)=f(x)-g(x) where f(2c)=3x2 l and g(x)=x3 +8,show that p'(x) f'(x)-g'(x) The expression for p(x) can be simplified to The Chain Rule If f and g are functions having derivatives, then the composite function h(x) = f (g(x)) has a derivative given by: Work from the outside to the inside. In words we say the derivative 0: the outer function evaluated at the inner function times the derivative of the inner function. In Liebniz Notation: If v is a function of u and u is a function of ); (so that v is a composite . N . dy _ dydu f. d)' :11! - tunctlon), then E $3? proncled that E and Ii? exust. \fThe position function of an object is given by 5(t) :t3 25f, where time, t, is in seconds. distance, 5, is in metres, and t 2 0. What is the acceleration at the instant the Object is momentarily at rest? a. Sin/s2 b. 9.sm/s2 c. iom/s2 d. 2m/s2 Mark: 3 The height function of a tossed baseball is given by h(t) = -4.9t2 + 14.7t + 2, where time: t is in seconds, height: h, is in metres, and t is greater than or equal to 0. What is the maximum height, to the nearest metre, reached by the baseball? a. 13111 b. 14m c. 20m d. 10m Mark: 3 This question requires a full and complete solution. '35 (x+1 2 Determine the equation of the line tangent to the function f(x) = at x=-2