Power Rule for 100Power Rule for 100

Given y = 2x, what is dy/dx?

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dy/dx = 2

Power Rule for 200Power Rule for 200

Given , what is y’?

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y’ = 6x

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23 1y x

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

'(2) 10f Push the Space Bar to check your answer.Push the Space Bar to check your answer.

( )( ) , (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

2 2Given 16, find by implicit differentiation. dyx y dx

xdy

dx y

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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

The points of intersection are (1, 2).

(1, 2), ' 1 & ' -1

(1, -2) ' -1 & ' 1

the graphs are orthogonal.

At y y

At y y

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2 2 2

Orthogonal Trajectories: Two graphs are orthogonal

if at their point(s) of intersection their tangent lines are

perpendicular to each other. Use your calculator to

show that 2 6 & 4 are orthox y y x gonal.