{ chapter 4 practice ap calculus. differentiate:
TRANSCRIPT
{Chapter 4 Practice
AP Calculus
Differentiate:๐๐๐ฅsec๐ฅ=ยฟ
๐๐๐ฅcsc๐ฅ=ยฟ
๐๐๐ฅtan ๐ฅ=ยฟ
๐๐๐ฅcot๐ฅ=ยฟ
๐๐๐ฅsinโ1๐ฅ=ยฟ
๐๐๐ฅsecโ1 ๐ฅ=ยฟ
๐๐๐ฅcscโ1๐ฅ=ยฟ
๐๐๐ฅtanโ 1๐ฅ=ยฟ
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
To the nearest thousandth, calculate the slope of the tangent where x = 4:
๐ฅ2โ4 ๐ฆ2=4
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
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
Derivatives Practice
๐๐๐ฅ
๐๐๐ 4(5 ๐ฅโ4 )
๐๐๐ฅ
7๐๐๐ 5๐ฅ
๐๐๐ฅx โ cscโ15๐ฅ
๐๐๐ฅ
๐3๐ฅ
7 ๐ฅโ4
Derivatives Practice
๐๐๐ฅ
๐๐๐ 4 (5๐ฅโ4 )=โ20 (cos (5 ๐ฅโ4 ) )3 โ sin (5 ๐ฅโ4 )
= 35 sec 5x tan 5x
=
=
Differentiate implicitly:
4 ๐ฅ2+ tan ๐ฅ๐ฆ=๐ฆ3
Differentiate implicitly:
Derivative:
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)
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