Download HW 3-4: The Chain Rule

HW 3 –4: The Chain Rule
Math 400
Name____________________
Find the first derivative for each function below. Use the y ′ notation for functions labeled y and the
f ′(x) notation for functions labeled f (x) .
Show all required steps.
1. f (x) = (3x − 5) 4
(
3. y = 6x 3 − 5x 2
5. y = 5 4x + 9
HW 3 – 4
)
−2
2.
f (x) = −2(−3x + 7) 3
(
)
4. y = 9 3x 2 − 2x + 1
6.
Page 1 of 9
y =6
3
2/3
3x 2 − x
©2013 Eitel
(
7.
f (x) = ln 5x 2 − 2x
9.
f (x) = e x
11.
8.
10.
6
ln (4x ))
(
f (x) =
HW 3 – 4
)
x
f (x) = ln(3 x + 7) 4
( )
f (x) = ln e 3x
12. f (x) = 4 5x −3
Page 2 of 9
©2013 Eitel
( )
13. f (x) = sin 3x 2
( )
15. f (x) = tan3 5x 2
17. f (x) =
HW 3 – 4
3
sin(2x)
14. f (x) = cos (sin(2x))
16. y = sin2 (cos(2x) )
( ( x ))
18. y = sin cos
Page 3 of 9
©2013 Eitel
19. f (x) = sin(3x) cos(3x)
20. f (x) = 3x 2 tan(5x)
Hint: Double abgle formula for sin(x)
21. f (x) = x 2 e 2x − 4 x e −x
HW 3 – 4
22.
Page 4 of 9
f (x) = x e 2x − ln
( x)
©2013 Eitel
23. f (x) = ( 3x − 1) 2 (4 x + 3)3
24.
(
) (2x2 + 3)
f (x) = x 2 − 1
HW 3 – 4
3
4
Page 5 of 9
©2013 Eitel
25. f (x) =
26.
f (x) =
HW 3 – 4
ln( x)
x2
x
2
x +1
Page 6 of 9
©2013 Eitel
x
27. f (x) = 3
x2 − 3
28.
f (x) =
HW 3 – 4
2x + 3
4x 2 + 9
Page 7 of 9
©2013 Eitel
29. f (x) =
(2x + 1)3
( 3x + 2)2
⎛ 2x 2 − 3x ⎞
30. y = ln ⎜
⎟
⎝ 2x − 1 ⎠
(
) ⎞⎟
⎛ x x2 + 3
31. y = ln ⎜
⎜ 3x − 5
⎝
HW 3 – 4
⎟
⎠
Page 8 of 9
©2013 Eitel
32.
Find f ′′(x)
f (x) = (2x − 7)3
33.
Find f ′′(5)
f (x) = 2x − 9
For each function below find the equation of the tangent line at the given x value. Use the
y − y1 = m( x − x1) form
34.
f (x) = 2tan3 ( x )
where x = π / 4
HW 3 – 4
2
35. f (x) 2x + 1
where x = −1
Page 9 of 9
©2013 Eitel