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CALCULUS: Graphical,Numerical,Algebraic by Finney,Demana,Watts and Kennedy Chapter 3: Derivatives 3.3: Derivative of a function pg. 116-126

A) Using a definition of the derivative find the derivative of y =x2 at x = a

B) Using a definition of the derivative find the derivative of y =x3 at x = a

C) Using a definition of the derivative find the derivative of y =x2 + 4 at x = a

What you'll Learn About How to find the derivative of: Functions with positive and negative integer powers Functions with products and quotients

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Find the derivative using the power rule

D) f(x) = 3 + x2 - x3 + x5 E) 74

35

xx

y

F) 3 xy G)

x

xxy

1

43

35

H) xx

xxf21

4)(

Find the Horizontal Tangents of each curve

I) x3 + 2x2 = 0 J) 032

5

3

2 23 xxx

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Using Algebra and the Product Rule to take a derivative

J) y = (x2 + 3)(x3 - x) J) y = (x2 + 3)(x3 - x)

Using Algebra and the Quotient Rule to take a derivative

K) x

xxf

9)(

3 K)

x

xxf

9)(

3

Take the Derivative of the function

L) y = (x2 + x + 2)(x5 + x3 + 5x)

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Take the Derivative of the function

M) 2

4

2)(

x

xxf

N) 12 35)(

xxxf

O) 31

43)(

xx

xxxf P)

1

1)(

3

3

x

xxf

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Find the equation for the tangent line at the given point

Q) 2

5 2

x

xxy

at x = 1 R) 35 2 xy at x = 3

S) Find an equation of the line perpendicular to the tangent to the curve

y =4x3 - 6x + 2 at the point (2, 22).

T) Find the points on the curve y = x3 - 3x2 - 9 where the tangent is

parallel to the x-axis

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U) Suppose u and v are differentiable functions at x = 2 and

u(2) = 3, ,3)2( u v(2)=1, 2)2( v

i) Find uvdx

d

ii) Find

v

u

dx

d

iii) Find uvvudx

d223

V) Find the derivative of y = x with respect to x

W) Find the derivative of y = x with respect to t

X) Find the derivative of y = x with respect to P

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CALCULUS: Graphical,Numerical,Algebraic by Finney,Demana,Watts and Kennedy Chapter 3: Derivatives 3.5: Derivatives of Trig Functions pg. 141-147

A) y = 5 + x2 - tanx B) y = xsinx

C) cot

4y C)

cot

4y

D)

cscsec

cossin

y

What you'll Learn About How to find the derivative of a trig function

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Find equations for the lines that are tangent and normal to the

graph of y = 2cosx at 4

x

Find the points on the curve y = cot x, 2

0

x , where the

tangent line is parallel to the line y = -2x.

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CALCULUS: Graphical,Numerical,Algebraic by Finney,Demana,Watts and Kennedy Chapter 3: Derivatives 3.6: Chain Rule pg.148-156

xsyD

xosyC

yBxyA

cotcxc )

3c )

4xsin ) sin )

2

2

2

What you'll Learn About How to find the derivative of a composite function

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cossin

1 )

cossin )

)2cos()2sin(5 )

433

2

xxyF

xxyE

xxyE

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5 )

1

)

1

)

4-3

3

2

3

2

xxyH

x

xyG

x

xyG

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21

1 )

6-3x )

3

54

xyJ

xyI

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csc3 )

csc3 )

xxyM

xxyL

3

cot9 if y Find N)

xy

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Suppose that functions f and g and their derivatives have the

following values at x = 2 and x = 3.

Evaluate the derivatives with respect to x

2 at x g(x)

f(x) ) 3 at x f(x)g(x) )

3 at x g(x)f(x) ) 2 at x 2f(x) )

DC

BA

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2 at x (x)g(x)f )

3 at x g

1 )

2 at x f(x) ) 2 at x g(x)f )

22

2

F

xG

FE

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CALCULUS: Graphical,Numerical,Algebraic by Finney,Demana,Watts and Kennedy Chapter 3: Derivatives 3.8: Derivatives of Inverse Trig Functions pg.165-171

Find the derivative of the inverse sine function using implicit differentiation

What you'll Learn About How to find the derivative of inverse functions

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sin5xrccscf(x) ) xarctanx-1x )

sinxarccosx )

x

1arccos ) xarcsin )

332

2

2

xaEyD

yC

yByA

Find the equation of the tangent line

2at x x csc ) -1 yF

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G) Find the derivative of f(x) = sinx at 6

x

H) Find the derivative of f(x) = arcsinx at 2

1x

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-144. f (2) -3, f (2) , and g(x) f ( ),

3

what is the equation of the tangent line to g(x)

at x -3?

-3 -3A) -2 x 3 B) 2 x 3

4 4

3 3) -2 x 3 D) 3 x 2

4 4

E) -

I f x

y y

C y y

y

4

2 x 33

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-1-45. f (2) -3, f (2) , and g(x) f ( ),

3

what is the equation of the tangent line to g(x)

at x -3?

-3 -3A) -2 x 3 B) 2 x 3

4 4

3 4) -2 x 3 D) 2 x 3

4 3

E)

I f x

y y

C y y

y

4

-2 x 33

-1-36. f (2) -3, f (2) , and g(x) f ( ),

4

what is the equation of the tangent line to g(x)

at x -3?

-3 -4A) -2 x 3 B) 3 x 2

4 3

3 4) -2 x 3 D) 2 x 3

4 3

E)

I f x

y y

C y y

y

-4

-2 x 33

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CALCULUS: Graphical,Numerical,Algebraic by Finney,Demana,Watts and Kennedy Chapter 3: Derivatives 3.9: Derivatives of Exponential and Logarithmic Functions

7 ) ex- )

) 5 )

5 ) )

6 ) 5 )

7 ) 5 )

22x443

4

35

5

3arctansin

2

xx

xx

xx

xx

xx

yBexyI

eyHeyG

eyFeyE

yDyC

yByA

What you'll Learn About How to take the derivative of exponential and logarithmic functions

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arcsinxlnln-xn )

5ln ) ln )

ln ) ln )

xlog

5 )

x

4log )

xlog ) xlog )

23

4

4

2

7

5

36

3

5

lxyI

xyHxyG

xyFxyE

yDyC

yByA

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CALCULUS: Graphical,Numerical,Algebraic by Finney,Demana,Watts and Kennedy Chapter 3: Derivatives 3.6/10.1: Derivatives of Parametric Equations

Graph the parametric function given

0 t ty 3-t ) 2 xA

B) Find the derivative of the function at t=5

C) Find the equation of the tangent line at t=1

9t y 3 2 tx

D) Find the equation of the tangent line at 4

sin y cos x

E) Find the equation of the tangent line at t

2tan y 1 - 2sec2 ttx

What you'll Learn About How to take the derivative of functions in Parametric Form

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A curve C is defined by the parametric equations

x = t2 – 4t +1 and y = t3. Determine the equation of the

line tangent to the graph of C at the point (1, 64)?

Determine the horizontal and vertical tangents for the

parametric curve

2sin2 cos x)

4t -tyt -1 ) 2

yB

xA

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The derivative of ex is: (Itself)(Derivative of the power)

The derivative of ax is:

(Itself)(ln of the base)(Derivative of the power)

The derivative of ax is: (Itself)(ln of the base)(Derivative of the power)

The derivative of ln u is:

(one over what you are taking the ln of) times now you should be in the

numerator (Derivative of what you are taking the ln of)

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When you do the power rule the base does not change

only the power

- Once you have done the power rule, you are done

with the powers

When you do the derivative of a trig function the angle

does not change

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