MAT 270 - Derivative Practice IIykim/mastery_practice_1.pdfsin x x y = 19. ( ) π 1 y = tan sinx +...

6
MAT 265 - Derivative Practice I Find the derivative of the following functions. 1. ( ) ( ) 5 2 4 3 − = x x f 2. ( ) ( ) x x x f 3 2 2 3 = 3. ( ) ( ) 3 1 2 4 3 + = − x e x f x 4. ( ) ( ) 3 1 2 2 − = x e x g x 5. ( ) ( ) ( ) 4 2 2 2 3 x x x x e x g x + − + + = 6. ( ) ( ) x x x f 5 3 2 5 2 − = 7. ( ) x y 3 cos =

Transcript of MAT 270 - Derivative Practice IIykim/mastery_practice_1.pdfsin x x y = 19. ( ) π 1 y = tan sinx +...

Page 1: MAT 270 - Derivative Practice IIykim/mastery_practice_1.pdfsin x x y = 19. ( ) π 1 y = tan sinx + 20. y ... sin 7 1 = − 39. x x x y csc2 ... cos 9 = 41. ( ) 37 1 y = sin tanx +

MAT 265 - Derivative Practice I

Find the derivative of the following functions.

1. ( ) ( )52 43 −= xxf

2. ( ) ( )xxxf 32 23=

3. ( ) ( ) 312 43 += − xexf x

4. ( )( ) 3

12

2

−=

x

exg

x

5. ( ) ( ) ( ) 422 23 xxxxexg x +−++=

6. ( ) ( )x

xxf

5

3252−

=

7. ( )xy 3cos=

Page 2: MAT 270 - Derivative Practice IIykim/mastery_practice_1.pdfsin x x y = 19. ( ) π 1 y = tan sinx + 20. y ... sin 7 1 = − 39. x x x y csc2 ... cos 9 = 41. ( ) 37 1 y = sin tanx +

8.

2

sin1

cos

−

=x

xy

9. ( )502 517 xxy −=

10. ( )( )xey x 3sin2=

11. xy sin=

12.1

tan2 −

=x

xy

13. ( )2arcsin xy =

14. ( ) ( )xxy arctan12 +=

Page 3: MAT 270 - Derivative Practice IIykim/mastery_practice_1.pdfsin x x y = 19. ( ) π 1 y = tan sinx + 20. y ... sin 7 1 = − 39. x x x y csc2 ... cos 9 = 41. ( ) 37 1 y = sin tanx +

15. ( )[ ]3arccos xy =

16. ( )xy 6tan=

17.x

xy

2cos

2sin=

18.2

sin

x

xy =

19. ( )π1

sintan += xy

20. ( ) ( )9sin35cos3 xxy +=

21. ( )123sin 23 +−= xxy

Page 4: MAT 270 - Derivative Practice IIykim/mastery_practice_1.pdfsin x x y = 19. ( ) π 1 y = tan sinx + 20. y ... sin 7 1 = − 39. x x x y csc2 ... cos 9 = 41. ( ) 37 1 y = sin tanx +

22.

=x

xy1

tan2

23. ( ) ( )xxf 2sin=

24. ( ) ( )xexg x 2cos3=

25. ( )[ ]43arcsin xy =

26. ( )16tan 2 −= xy

27. ( ) xey 3sin=

28.3

22 tansec

x

xxy

−=

Page 5: MAT 270 - Derivative Practice IIykim/mastery_practice_1.pdfsin x x y = 19. ( ) π 1 y = tan sinx + 20. y ... sin 7 1 = − 39. x x x y csc2 ... cos 9 = 41. ( ) 37 1 y = sin tanx +

29.3

cos

x

xy =

30. ( )( )e

xy1

4sinsin +=

31. ( )xxy 73cos 22 −=

32.

=x

xy1

sin3

33. ( )xy 4cos=

34.12

tan

−=x

xy

35. 3 1sin −= xy

Page 6: MAT 270 - Derivative Practice IIykim/mastery_practice_1.pdfsin x x y = 19. ( ) π 1 y = tan sinx + 20. y ... sin 7 1 = − 39. x x x y csc2 ... cos 9 = 41. ( ) 37 1 y = sin tanx +

36. ( ) 23sin π+= xexy

37.xx ee

y−+

=π

38. xxy cos6

1sin

7

1−=

39.x

xxy

22 cotcsc −=

40.( )( )xx

y9sin

9cos=

41. ( )37

1tansin += xy

42.

−=

xxy

1tan4 5


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