Calculus I
Finding Derivatives – More Practice!
Find each derivative. Simplify your answers.
1. y = -2x 2 + 3x – 6
2. y =
2
3x 2
3. f(x) =
x
x
1
x2
4
x -3
5. y = x 3 – 3x – 2x-4
6. y = x +
1
7. y = 2 + 4 x
x
2x 2 – 3x + 1
8. y =
x
x 2 + 3x
9. y =
6
4. y =
11. y =
x+1
x–1
12. y =
x+1
x
4x 3 2
13. y =
x
14. y =
3x – 2
2x – 3
15. V =
4 3
πr
3
16. s = -16t 2 + 128t
17. y = x 3 – 3x 2x 2 + 3x + 5
10. y =
x
x–1
(
)(
)
18. y = -3x 2 3
Solutions:
1. -4x + 3
8. 2 –
14. -
1
x2
5
( 2x – 3)2
2
2
1
8
2
4. 12x 2
5. 3x 2 – 3 + 5
6. 1 – 3
7. - 3 +
32
x
2x
x
x
x
2
1
1
1
1
2
9. x +
10. 11. 12. - 2
13.
2
2
3
2
x
x
( x – 1)
( x – 1)
2
15. 4πr 2
16. -32t + 128
17. 10x 4 + 12x 3 – 3x 2 – 18x – 15
18. - 3
x
2. −
4
3x 3
3. −