Worksheet 3B
dy
Find
for the following equations:
dx
( x + 5)3 (2x − 7)
4
1. y =
(sin x )
e+1
2. y = 3
3. y = 6sec x
4. y = ln(ln(tan x 2 ))
5. y = sec−1 (3x 3 )
6. y = ln x ln x
7. y = x 2 y 2 − sin(xy)
8. y = log 4 (5x 2 )
2
9. y = 2tan(sin(3x)) − eln x
10. y = sin3 ( cos( 2x ))
11. Find an equation for the line tangent to the
graph
5π
y = 3tan x + 3 at x =
4
12. The motion of a particle is given by
2
s(t) = −9t + 4t + 6 (s in feet and t in
seconds). Find when the instantaneous
velocity is equal to the average velocity
from t = 2 seconds to t = 4 seconds. Be
sure to show your work!
Worksheet 3B-2
Review 3B
dy
for the following equations:
dx
1. y = tan−1 (6x 2 )
2x
2. y = 5 e
3. y = 5csc 4 ( x + 2)
4. y = ln(8x 3 )
5. y = log 4 (sin−1 x)
6. y = tan(tan−1 (4 x 7 + 2x 5 ))
2
7. y = x ln x
4 cosx
8. y =
8x 4
9. x = xy 2 + cos(x 2 y)
10. y = ln(x cosx )
Find
dy
for the following equations:
dx
1. y = sec−1 (2x)
2. y = 2e x +1
3. y = tan2 ( x 2 )
Find
4. y = log 5 (x 4 )
5. y = cos−1 (9x 2 )
6. y = cot3 (ln( 2x ))
7. y = 4ln(3x) − e x+ 1
8. y = 4x ⋅5ln x
9. 6 = xy − tan(xy)
10. y = x sin x
11. Find an equation for the line tangent
to the graph
7
5π
y = sin x + at x =
2
6
EXTRA PRACTICE
1. y = ( x 2 + x − 3)
2. y = sec
2
3
9. y = tan(sin(x ))
2
10. y = 3x 2 (5x 2 + 5)
x
3. y = x 2 + 2x
cos(3x) ⎞
4. y = ⎛⎝
4x + sin x ⎠
3
5. y = (6 + tan( x 2 ))
6. y = 3 csc(2x)
7. y = 4x 4 (5x 2 + 4 )
1
8. y =
sec x + tan x
3
11. y = ( 2x − x )
x2
12. y =
1− x 2
2
2
12. The motion of a particle is given by
2
s(t) = −16t + 24t + 96 (s in feet and
t in seconds). Find when the
instantaneous velocity is equal to the
average velocity from t = 0 seconds
to t = 3 seconds. Be sure to show
your work!