{ Chapter 4 Practice AP Calculus. Differentiate:
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Transcript of { Chapter 4 Practice AP Calculus. Differentiate:
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{Chapter 4 Practice
AP Calculus
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Differentiate:๐๐๐ฅsec๐ฅ=ยฟ
๐๐๐ฅcsc๐ฅ=ยฟ
๐๐๐ฅtan ๐ฅ=ยฟ
๐๐๐ฅcot๐ฅ=ยฟ
๐๐๐ฅsinโ1๐ฅ=ยฟ
๐๐๐ฅsecโ1 ๐ฅ=ยฟ
๐๐๐ฅcscโ1๐ฅ=ยฟ
๐๐๐ฅtanโ 1๐ฅ=ยฟ
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Differentiate: sec x tan x
-csc x cot x
๐๐๐ฅtan ๐ฅ=๐ ๐๐2๐ฅ
๐๐๐ฅcot๐ฅ=โ๐๐ ๐2๐ฅ
๐๐๐ฅsinโ1๐ฅ=
1
โ1โ๐ฅ2
๐๐๐ฅcscโ1๐ฅ=โ
1
ยฟ๐ฅโจโ๐ฅ2โ1
๐๐๐ฅtanโ 1๐ฅ=
1
๐ฅ2+1
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To the nearest thousandth, calculate the slope of the tangent where x = 4:
๐ฅ2โ4 ๐ฆ2=4
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To the nearest thousandth, calculate the slope of the tangent where x = 4:
๐ฅ2โ4 ๐ฆ2=4Differentiate implicitly:
2 ๐ฅ โ๐๐ฅ๐๐ฅโ8 y โ
๐๐ฆ๐๐ฅ
=0
ยฟโ8 y โ๐๐ฆ๐๐ฅ
=โ2 ๐ฅ
ยฟโ8 y โ๐๐ฆ๐๐ฅ
=โ2๐ฅโ8 ๐ฆ
โ๐๐ฆ๐๐ฅ
=๐ฅ4 ๐ฆ
Find coordinates of y when x = 4and substitute into dy/dx equation:
h๐ ๐๐๐ฅ=4 , ๐ฆ=ยฑโ3๐๐ฆ๐๐ฅ
=44ยฟยฟ
๐๐ฆ๐๐ฅ
=44ยฟยฟ
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โข Be prepared for NO CALCULATOR section!โข Basic chain rule, product rule, quotient ruleโข Basic trig derivativesโข Inverse trig derivativesโข Implicit differentiation โข Use limits to find values to make a
piecewise function differentiable (and continuous).
โข Related Rates
Ch. 4 Test Review Topics
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Derivatives Practice
๐๐๐ฅ
๐๐๐ 4(5 ๐ฅโ4 )
๐๐๐ฅ
7๐๐๐ 5๐ฅ
๐๐๐ฅx โ cscโ15๐ฅ
๐๐๐ฅ
๐3๐ฅ
7 ๐ฅโ4
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Derivatives Practice
๐๐๐ฅ
๐๐๐ 4 (5๐ฅโ4 )=โ20 (cos (5 ๐ฅโ4 ) )3 โ sin (5 ๐ฅโ4 )
= 35 sec 5x tan 5x
=
=
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Differentiate implicitly:
4 ๐ฅ2+ tan ๐ฅ๐ฆ=๐ฆ3
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Differentiate implicitly:
Derivative:
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Useful Related Rates Formulas
๐ถ๐๐๐๐๐๐๐ข๐๐ :๐=13๐ ๐2h
๐ถ๐๐๐๐๐ ๐ด๐๐๐ :๐๐2
Cylinder Volume: V =
h๐๐ฆ๐ก ๐๐๐๐๐๐๐ h๐ ๐๐๐๐๐ :๐2+๐2=๐2
๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐ (๐๐๐ก ๐ข๐๐๐๐๐๐๐๐ก๐๐๐)
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Ch. 4 R Problems, pg. 180: R4 ad, R5a, R6, R8b, R9 (pretty hard)
Suggested Review
Additional ReviewOnline videos, PPTSExamples from notes4.2 #1-15 odd, 4.3 1-19 odd4.4 1-25 odd, 4.5 13-23 odd