100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 differentiation jeopardy 100 200 300 400...
TRANSCRIPT
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Differentiation Jeopardy
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Power Rule Product Rule Quotient Rule Chain Rule Implicitly
A Review of Chapter 3
Power Rule for 100Power Rule for 100
What is dy/dx?
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xy 5cos 5ln55sin' xxy
Power Rule for 200Power Rule for 200
What is y’?
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x
xy1
sin2cos
2
11cos2sin2'
xxxy
Power Rule for 300Power Rule for 300
Given ,
find the slope of the tangent line to this function at the point (-1,7).
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m = 8
26 4 9y x x
Power Rule for 400Power Rule for 400
Given , find the slope of the tangent line to this function at the point (2,72).
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m = 120
3 214 12 8y x x
Power Rule for 500Power Rule for 500
Given ,
find the equation for the tangent line of this function at (-3,33).
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y = -32x - 63
26 4 9y x x
Final
Product Rule for 100Product Rule for 100
Given 23 (2 1),y x x
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dy/dx = 18x^2 + 3
/ ?dy dx
Product Rule for 200Product Rule for 200
Given y=sin cos ,
2 2y=cos sin
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what is / ?dy d
2 2cos sin ????? cos 2x
Product Rule for 300Product Rule for 300
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m = -1
Given y=2sin cos , 3
find the slope of the tangent line to this function at ( , ).3 2
Product Rule for 400Product Rule for 400
Given , determine the point(s) at which the graph of the function has a horizontal tangent.
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(0,0) & (2,4)
2 ( 1)y=x ( 1)x
Product Rule for 500Product Rule for 500
Given , find an equation of the tangent line to f at (1,-3).
3f(x)=(x 3 1)( 2)x x
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'( ) 2f x x
Final
Quotient Rule for 100Quotient Rule for 100
2
3'( )
(4 1)f x
x
3 , '( ).
4 1
xGiven find f x
x
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Quotient Rule for 200Quotient Rule for 200
2
sin cos/
t t tdy dx
t
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cos , / .
tGiven y find dy dt
t
Quotient Rule for 300Quotient Rule for 300
3
2
3 2( )
1
x xf x
x
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Given , find the slope of the tangent
line to this function at (-2,-4).
1
3m
Quotient Rule for 400Quotient Rule for 400
Given , find the slope of the tangent
to f at the point .
sin( )
xf x
x
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2( , )2
2
4m
Quotient Rule for 500Quotient Rule for 500
Find '(2) given the following: f
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( )( ) , (2) 3, '(2) 2, (2) 1, & '(2) 4.
( )
g xf x g g h h
h x
Final
Chain Rule for 100Chain Rule for 100
3Find the first derivative of (2 7) . y x
2' 6(2 7)y x Push the Space Bar to check your answer.Push the Space Bar to check your answer.
Chain Rule for 200Chain Rule for 200
Find the slope of the tangent line of
sin(3 ) at the origin.y
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3m
Chain Rule for 300Chain Rule for 300
Find the first derivative of sin(cos ).y
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/ sin cos(cos )dy dx
Chain Rule for 400Chain Rule for 400
2
Find an equation of the tangent line to the graph of
3 2
at the point (3,5).
y x
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9 2
5 5y x
Chain Rule for 500Chain Rule for 500
2
Find an equation of the tangent line to the graph of
tan
at the point ( ,1).4
y
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4 ( 1)y x Final
Implicit Differentiation for 100Implicit Differentiation for 100
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Given 2x3 = 2y2 + 5, find dy/dx.
dy/dx 3x2 /2y
Implicit Differentiation for 200Implicit Differentiation for 200
3 2Given 4, find by implicit differentiation. dyx xy y dx
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23 2
y xdydx y x
Implicit Differentiation for 300Implicit Differentiation for 300
2 3Given 0, find by implicit differentiation and evaluate the derivative at (1,1).
dyx y dx
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2At (1,1) : 3
dydx
Implicit Differentiation for 400Implicit Differentiation for 400
2Given the Witch of Agnesi function: ( 4) 8,
find the slope of the tangent line to the graph at (2,1).
x y
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1At (2,1) :
2m
Implicit Differentiation for 500Implicit Differentiation for 500
2 2
Find equations for the tangent line and normal line
to the circle +y =25 at ( 3, 4).x
(The normal line at a point is perpendicular to
the tangent line at the point.)
3 25Tangent Line:
4 4y x
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4Normal Line:
3y x
Final
FINAL JEOPARDYFINAL JEOPARDY
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Question
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Question