Derivative Review Part 1

3.3,3.5,3.6,3.8,3.9

Find the derivative of the function

xx4

1

8

1xy )1 25

p. 181 #1

Find the derivative of the functionp. 181 #3

2sinxcosxy )3

Find the derivative of the functionp. 181 #3

2sinxcosxy )3

Find the derivative of the functionp. 181 #4

1-2x

12xy )4

Find the derivative of the functionp. 124 #4

xx

3

y )23

Find the horizontal tangent to curvep. 124 #7

12y )7 23 xxx

Find the derivative of the functionp. 124 #13

)1)(1(y )13 2 xx

Find the derivative of the functionp. 124 #13

)1)(1(y )13 2 xx

Find the derivative of the functionp. 124 #17

23

52y )17

x

x

Find the derivative of the functionp. 124 #29

184y )29 2 xx

Find the derivative of the functionp. 124 #30

1234

y )30 1234

xxxx

a) Find all points where f has horizontal tangentsp. 126 Quick Quiz 4

24 4)( xxxf

a) Find an equation of the tangent line at x = 1.p. 126 Quick Quiz 4

24 4)( xxxf

b) Find an equation of the normal line at x = 1.p. 126 Quick Quiz 4

24 4)( xxxf

Find p. 146 4

xxy sec

dx

dy

Find p. 146 6

xxxy tan3

dx

dy

Find p. 146 8

x

xy

cos1

dx

dy

Find p. 146 8

x

xy

cos1

dx

dy

Find p. 153 17

xxy 4tansin 3

dx

dy

Find p. 153 19

12

3

xy

dx

dy

Find p. 153 21

23sin 2 xy

dx

dy

Find p. 153 24

xy 5tan

dx

dy

Find Extra Practice

xy 5tan

dx

dy

Find the derivative of y with respect to the given variable

p. 156 Quick Quiz #1

xy 3sin 4

Find the derivative of y with respect to the given variable

p. 170 #3

ty 2sin 1

Find the derivative of y with respect to the given variable

Extra Practice

ty 2sin 1

Find the derivative of y with respect to the given variable

p. 170 #21

xxy 121 csc1tan

Findp. 178 #8

xx xeexy 2

dx

dy

Findp. 178 #13

xy csc3

dx

dy

Findp. 178 #16

2ln xy

dx

dy

Findp. 178 #19

xy lnln

dx

dy

Findp. 178 #21

24log xy

dx

dy

Find the derivative of the functionp. 181 #8

12 xxy

Find the derivative of the functionp. 181 #11

xxy csc2

Find the derivative of the functionp. 181 #17

xy arccosln

Find the derivative of the functionp. 181 #24

21arcsin xy

Find the derivative of the functionp. 182 #30

2

cos1

sin1

x

xy

Suppose that the functions f and g and their first derivatives have the following values at x = -1 and x =0Find the first derivative of the following

p. 183 #67d

))(( xgf

x f(x) g(x)

-1 0 -1 2 1

0 -1 -3 -2 4

)(xf )(xg

1. Let f be a differentiable function such that f(3) = 15, f(6) = 3, and The function g is differentiable and g(x) = f-1(x) for all x. What is the value of a) -1/2 b) -1/8 c) 1/6 d) 1/3e) The value of cannot be determined

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

3what is the equation of the tangent line to g(x)

at x -3?

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

4 43 3

) -2 x 3 D) 3 x 24 4

E) -

I f x

y y

C y y

y

42 x 3

3

Find the equation of the tangent and normal line to the curve at the given point

p. 92 #11

2at x 1

1

x

y

Find the equation of the tangent and normal line to the curve at the given point

p. 92 #11

0at x 1-3x-2 xy

Find the equation for the line tangent to the curve at the given value of t

p. 182 #51

6at t tan5 sec3

tytx

Find the points at which the tangent line to the curve is horizontal and/or vertical

p. 535 #25

4t - 2 3tytx

1. A curve C is defined by the parametric equations x = t2 – 4t +1 and y = t3. Find

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

2 22. If ( ) ln , then, ( )f x x f e

1. A curve C is defined by the parametric equations x = t2 – 4t +1 and y = t3. Find the equation of the line tangent to the graph of C at the point (-2, 27)?

2. Let h be a differentiable function, defined by f(x) = h(x3– 4). Find .(3)f