Mathematics II

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Derivative Practice


Mathematics 1 (Vaal University of Technology)




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Practice Problems on Derivative Computing (with Solutions)

This problem set is generated by Di. All of the problems came from past exams of Math 221. For
derivative computing – unlike many of other math concepts – more lectures do not help much, and
nothing compares to practicing on one’s own! The idea of this problem set is to get enough practice,
till the point that it becomes hard to make any mistake. :)

√
3
1. y = x2 sin x
tan x
2. y = x3 +2

3
3. y = x4 + sin x cos x
x3 −2x
4. y = x+3
√ 10
5. y = x2 − 1 + 1
√
6. y = cos x2 tan x + 1




7. y = cos (cos (cos (3x)))
q
8. y = 1+x
2−x
√
9. y = x2 ( x + 2)
√ 4π


10. f (x) = 2 x2 + 1 + sin 5
sin x
11. h (x) = 2x−3
1 2
12. y = x3 + 2x3
− √
3x


13. y = sin (5x) cos (3x)

4
14. y = cos x2 + cos2 x



15. y = 12 + x cos x + x5

16. y = x2 + x − 1 sin x cos2 x



 
17. y = cos x2 + x+1x


x2 −2
18. y = x4 +1
√
19. y = x2 3 tan x
√ 5
20. y = x2 + 1 + x
√
21. y = 1 − cos x (tan x)3
sin(x3 )
22. y = sin(x2 )

23. y = x3 + sin (x) cos2 (x)

1




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