Dr. Byrne Fall 2012
3.1
Exam 2 Review Topics – Differentiation
the limit definition of the derivative
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Be able to find the derivative of a function using the limit definition (#5,7,9,13,27,29)
Be able to derive where the limit definition comes from (as the slope of the function at a point)
(quiz)
Given the slope of a function, be able to find the equation for the tangent line (#5,7,9,13)
3.2
matching or generating the graph of the slope of a function from the graph of a function, or the
graph of a function from the graph of its slope (#27—30)
3.3
Differentiation Rules – know how to use these quickly and accurately but the formulas will be
provided
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3.5
Power Rule
Product Rule
Quotient Rule
e^x
Tip: sometimes you don’t need to apply the quotient rule by breaking up a fraction (#25,45,49)
Being able to choose a parameter to make a function differentiable (#69)
Derivatives of Trig Functions
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3.6
CHAIN RULE!!
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3.7
Be able to use the power rule, product rule, quotient rule (and quotient rule) with trig
expressions but again the formulas will be provided
Be able to derive the derivative of tangent, cotangent, secant and cosecant using only
the derivatives for sine or cosine
On the exam you will not need to simplify your answers with a lot of complicated
algebra; the answer will be correct if you’ve taken the derivative correctly; however, no
problem given in the homework is too complicated to appear on the exam – make sure
you can do all of them
Implicit Differentiation
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Be able to find the derivative of a function using implicit differentiation
Be able to find the tangent or normal line of a curve at a point
3.8
derivatives of inverse functions
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Given the formula for the derivative rule for inverses, be able to find the derivative of
the inverse of a function (#7)
Be able to derive the derivative of ln(x) from the formula and the derivative of e^x
Be able to find derivatives of functions with ln(x) (#15,17,19,21,33,55)
Be able to apply logarithmic differentiation and recognize when it would be effective to
do so (for example, which problems in section 3.3 or 3.6 would be easier now?)
(#43,45,51)
Be able to find the derivative of a function with the variable in the exponent
(#69,89,93)
3.9
inverse trig functions – given the formula be able to find the derivative of an inverse trig
function (using the chain rule if necessary) (#21,25,31,33,39,41)
3.10
Related Rates (#23,25,31, problems on the worksheet)
3.11
Linearization and Differentials
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given a function, find the linearization F(x) (#1,3,5)
And use the linearization to approximate the value of a function at a point (#7,9,11,13)