AP Calculus BC
Chapter 4 Review
Topics:
Chain Rule
Inverse Trig Derivatives
Mathematician:
10/7/13
Implicit Differentiation
Derivatives of Logarithms
Parametric Derivatives
Derivatives of Exponentials
1)
Find
dy
1
when y = xe 4 x - 3x + x 3
dx
4
2)
Find
dy
when y  log2 3x  1
dx
3)
Find
dr
when r  tan2 (  2)
d
4)
Find
dy
when x 2  sin(xy )  y
dx
5)
Find
dy
when y = (sin x )x
dx
6)
Find
dy
when y = cos-1 (x 2 )
dx
7)
-x
dy
Find
when y = 10e 5 + ln2 x
dx
8)
Find
æ secθ ö
dr
when r = ln çç 2 ÷÷÷
çè θ ÷ø
d


9)
Find
dy
when x  cos(x  y )  0 .
dx
a) csc( x  y )  1
10)
Find
b) csc( x  y )
x
sin( x  y )
d)
dy
when y  (4x  1)(1  x )3
dx
A) (1  8x )(1  x )2
B) (1  16x )(1  x )2
1
1 x
C) (7  16x )(1  x )2
e)
2
1  sin x
sin y
D) 3(4x  1)(1  x )2
dy
when 3x 2  2xy  5y 2  1
dx
11)
Find
A)
3x  y
x  5y
12)
If y = x ln3 x , then y ' =
(A)
c)
B)
3ln2 x
3x  y
x  5y
2
(B) 3ln x
x
C)
3x  5y
(C) 3(ln x  1)
D)
3x  4y
x
2
3
(D) 3x ln x  ln x
(E) None
x 
dy
.
 , find
dx
2
13)
If y  tan 1 
(A)
4
4+x2
(B)
1
2 4x2
(C)
2
4 x2
(D)
1
2+x2
(E)
2
4+x2
Use the following table for questions 14 -18.
x
0
1
2
3
f
2
4
5
10
f’
1
2
3
4
g
5
3
6
0
g’
-4
-3
-2
-1
14)
If A  g (f (x )) , find A '(0).
15)
If B 
17)
If D  f (x 3 ) g (x ) , find D '(1) .
19)
a)
Find the equation of the line tangent to the curve x 2  2xy  2y 2  5 at (1, 1).
b)
Find
1
, find B '(0) .
g (x )
16)
If C  g (2x ) , find C '(1) .
18)
If E  f (x )  3 g (x ) , find E '(3) .
d 2y
when x 2  2xy  2y 2  5 at the point (1, 1).
2
dx
20)
21)


2
Let f (x )  ln 1  x .
A)
State the domain of f (x ) .
B)
Find f '(x ) .
C)
State the domain of f '(x ) .
A particle moves along the x-axis with position at time t given by x (t )  e 2t sint for
0  t  2 . Find each time t, 0  t  2 , for which the particle is at rest.
22)
At what point on the graph of y  2e x  1 is the tangent line perpendicular to the line
y  3x  2 ?
23)
x 
 at the point x =
2
Find an equation for the tangent to the graph of y  sin 1 
3.