<p> MTH 251 - CALCULUS EXAM II REVIEW</p><p>2.7 Derivatives and Rates of Change • Be able to use the definitions at the bottom of pages 143 and 144 to find the slope of the tangent line at a point. • Be able to use the definitions at the bottom of page 146 to find the derivative of a function at a particular value of x = a. • Be able to find the equation of the tangent line to a curve at a point. • Be able to find the instantaneous velocity of an object using the limit definition.</p><p>2.8 The Derivative as a Function • Be able to find the derivative of a function using the limit definition. • Be able to graph the derivative of a function, given a graph of the function. • Be able to graph the derivative of a function, given the equation of the function. • Be able to find determine where a function is not differentiable and given reasons.</p><p>3.1 Derivatives of Polynomial and Exponential Functions • Be able to calculate derivatives of functions using the constant rule, power rule, constant multiple rule, sum and difference rules. • Be able to calculate derivatives of exponential functions. • Be able to find the equation of the tangent line to a function at a point. • Be able to find the equation of the normal line to a function at a point. • Be able to determine where a function has a horizontal tangent line.</p><p>3.2 The Product and Quotient Rules • Be able to determine derivatives of functions using the product and quotient rules. • Be able to find the equation of the tangent line to a function at a point. • Be able to find the second derivative of a function at a point. • Be able to find the equation of the normal line to a function at a point.</p><p>3.3 Derivatives of Trigonometric Functions • Be able to determine the derivatives of all 6 of the trigonometric functions. • Be able to find the derivative of a function involving trigonometric, polynomial and exponential functions using the product and quotient rules. • Be able to find the equation of the tangent line to a function at a point. • Be able to evaluate limits involving trigonometric functions. 3.4 The Chain Rule • Be able to separate a composite function into its inner and outer functions. • Be able to calculate derivatives using the chain rule and the derivative rules learned in the previous sections. • Be able to find the equation of the tangent line to a function at a point. • Be able to calculate the derivative of a composite function given information about the inner and outer functions and their derivatives.</p><p>3.5 Implicit Differentiation • Be able to find the derivative of a function both explicitly and implicitly and show that they are equal. • Be able to find the equation of the tangent line to a function at a point using implicit differentiation. • Be able to calculate the second derivative of a function using implicit differentiation. • Be able to calculate derivatives involving the inverse trigonometric functions.</p><p>3.6 Derivatives of Logarithmic Functions • Be able to calculate first and second derivatives of functions involving logarithms. • Be able to find the equation of the tangent line to a function at a point. • Be able to use logarithmic differentiation to find the derivative of a function.</p><p>Chapter 2 Review (p. 168) 35, 39, 41, 43, 45, 47</p><p>Chapter 3 Review (p. 265) 1 – 19 odd, 23, 25, 27, 29, 31, 35, 37, 39, 41, 49, 51, 53, 57, 59, 61, 63, 65, 69, 71, 73, 81, 83, 107</p>