Calculus Fall 2010 Lesson 16 (Product Rule & Quotient Rule)



Lesson Plan #16Class: AP CalculusDate: Monday October 17th, 2011Topic: Quotient Rule and Product RuleAim: How can we find the derivative of a quotient of 2 differentiable functions?Objectives: Students will be able to find the derivative of a quotient of 2 differentiable functions.Students will be able to find the derivative of a product of 2 differentiable functions.HW# 16: Differentiate and simplify as much as possible.1) 2) Do Now:The velocity of an automobile starting from rest is given by , where is measured in feet per second. What do we need to do to find the acceleration at 5 seconds?Write the Aim and Do NowGet students working!Take attendanceGive back workGo over the HWCollect HWGo over the Do NowAs of yet, we don’t have a rule for the derivative of a function that is the quotient of 2 differentiable functions. So let’s define a formula, called the quotient rule for derivatives, to do that.Quotient Rule: The derivative of the quotient of two differentiable functions f(x) and g(x) is given by, For the proof, use the definition of the derivative leading to the equationSimplify the complex fraction and use the properties of limits to obtain the above expressionExercises:1) Differentiate each functionA) B) 2) Find an equation of the line tangent to the curve at the point The function measures the percentage of the normal level of oxygen in a pond, where is the time in weeks after organic waste is is dumped into the pond. Find the rate of change of with respect to when A) B) C) Consider the following function which is a product of 2 functions:. Instead of multiplying out first, then using the power rule, we have a rule for the derivative of a function that is the product of two functions.Exercises:Find the derivative of .2) Find the derivative of Sample Test Questions:If , find Find if If , find A) B) C) D) E) None of the other choicesChoose the alternative that is the derivative dydx, of the function y=2-x3x+1-7(3x+1)2 B) 6x-5(3x+1)2C) -9(3x+1)2D) 7(3x+1)2 E) 7-6x(3x+1)2 5) Limit Review – Evaluate the limitsA) limx→∞5x4+2xx2 B) limx→0+x|x| C) limx→0-x|x| D) limx→∞10x2+25x+1x4-86) Continuity Review 3x2-11x-4, x≤4For what value(s) of k is the function f(x)= continuous at x=4 kx2-2x-1, x>47) Differentiation ReviewFind f'(x) if fx=4x3-3x25x7+1 ................
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