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