Chain Rule Bronze

Chain Rule Bronze

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Question 1 of 25

1. Question
Differentiate using the chain rule: \({\left(4{x}^{2}-3\right)}^{2}\)
- \(16x\left(4{x}^{2}-3\right)\)
- \(3\left(8x\right)\)
- \(16x\left(8x+3\right)\)
- \(3\left(4{x}^{2}+3\right)\)
Correct

Incorrect
Question 2 of 25

2. Question
Differentiate using the chain rule: \({\left(3{x}^{2}-1\right)}^{3}\)
- \(18x{\left(3{x}^{2}-1\right)}^{2}\)
- \(3{\left(6x\right)}^{2}\)
- \(3{\left(3{x}^{2}-1\right)}^{2}\)
- \(18x{\left(6x-1\right)}^{2}\)
Correct

Incorrect
Question 3 of 25

3. Question
Differentiate using the chain rule: \({\left(4{x}^{3}-5\right)}^{3}\)
- \(36{x}^{2}{\left(4{x}^{3}-5\right)}^{2}\)
- \(3{\left(4{x}^{3}-5\right)}^{2}\)
- \(36{x}^{2}{\left(12{x}^{2}-5\right)}^{2}\)
- \(3{\left(12{x}^{2}\right)}^{2}\)
Correct

Incorrect
Question 4 of 25

4. Question
Differentiate using the chain rule: \({\left(7x-5\right)}^{3}\)
- \(21{\left(7x-5\right)}^{2}\)
- \(14\left(7+5\right)\)
- \(2\left(7x+5\right)\)
- \(2\left(7\right)\)
Correct

Incorrect
Question 5 of 25

5. Question
Differentiate using the chain rule: \({\left(3{x}^{3}+9\right)}^{3}\)
- \(27{x}^{2}{\left(3{x}^{3}+9\right)}^{2}\)
- \(18{x}^{2}\left(9{x}^{2}+9\right)\)
- \(2\left(9{x}^{2}\right)\)
- \(2\left(3{x}^{3}+9\right)\)
Correct

Incorrect
Question 6 of 25

6. Question
Differentiate using the chain rule: \({\left(7x+6\right)}^{3}\)
- \(21{\left(7x+6\right)}^{2}\)
- \(3{\left(7x+6\right)}^{2}\)
- \(21{\left(7+6\right)}^{2}\)
- \(3{\left(7\right)}^{2}\)
Correct

Incorrect
Question 7 of 25

7. Question
Differentiate using the chain rule: \({\left(9x+8\right)}^{3}\)
- \(27{\left(9x+8\right)}^{2}\)
- \(3{\left(9x+8\right)}^{2}\)
- \(3{\left(9\right)}^{2}\)
- \(27{\left(9+8\right)}^{2}\)
Correct

Incorrect
Question 8 of 25

8. Question
Differentiate using the chain rule: \({\left(2{x}^{2}-8\right)}^{3}\)
- \(12x{\left(2{x}^{2}-8\right)}^{2}\)
- \(3{\left(4x\right)}^{2}\)
- \(12x{\left(4x+8\right)}^{2}\)
- \(3{\left(2{x}^{2}+8\right)}^{2}\)
Correct

Incorrect
Question 9 of 25

9. Question
Differentiate using the chain rule: \({\left(7{x}^{2}+8\right)}^{3}\)
- \(42x{\left(7{x}^{2}+8\right)}^{2}\)
- \(3{\left(7{x}^{2}+8\right)}^{2}\)
- \(3{\left(14x\right)}^{2}\)
- \(42x{\left(14x+8\right)}^{2}\)
Correct

Incorrect
Question 10 of 25

10. Question
Differentiate using the chain rule: \({\left(4{x}^{2}-7\right)}^{2}\)
- \(16x\left(4{x}^{2}-7\right)\)
- \(2\left(8x\right)\)
- \(16x\left(8x+7\right)\)
- \(2\left(4{x}^{2}+7\right)\)
Correct

Incorrect
Question 11 of 25

11. Question
Differentiate using the chain rule: \({\left(2{x}^{2}+1\right)}^{2}\)
- \(8x\left(2{x}^{2}+1\right)\)
- \(2\left(4x\right)\)
- \(2\left(2{x}^{2}+1\right)\)
- \(8x\left(4x+1\right)\)
Correct

Incorrect
Question 12 of 25

12. Question
Differentiate using the chain rule: \({\left(5{x}^{2}-8\right)}^{3}\)
- \(30x{\left(5{x}^{2}-8\right)}^{2}\)
- \(30x{\left(10x+8\right)}^{2}\)
- \(3{\left(5{x}^{2}+8\right)}^{2}\)
- \(3{\left(10x\right)}^{2}\)
Correct

Incorrect
Question 13 of 25

13. Question
Differentiate using the chain rule: \({\left(7{x}^{2}-5\right)}^{2}\)
- \(28x\left(7{x}^{2}-5\right)\)
- \(28x\left(14x+5\right)\)
- \(2\left(14x\right)\)
- \(2\left(7{x}^{2}+5\right)\)
Correct

Incorrect
Question 14 of 25

14. Question
Differentiate using the chain rule: \({\left(7{x}^{3}+3\right)}^{2}\)
- \(42{x}^{2}\left(7{x}^{3}+3\right)\)
- \(42{x}^{2}\left(21{x}^{2}+3\right)\)
- \(2\left(21{x}^{2}\right)\)
- \(2\left(7{x}^{3}+3\right)\)
Correct

Incorrect
Question 15 of 25

15. Question
Differentiate using the chain rule: \({\left(7{x}^{2}-7\right)}^{3}\)
- \(42x{\left(7{x}^{2}-7\right)}^{2}\)
- \(3{\left(7{x}^{2}+7\right)}^{2}\)
- \(3{\left(14x\right)}^{2}\)
- \(42x{\left(14x+7\right)}^{2}\)
Correct

Incorrect
Question 16 of 25

16. Question
Differentiate using the chain rule: \({\left(3{x}^{3}+5\right)}^{2}\)
- \(18{x}^{2}\left(3{x}^{3}+5\right)\)
- \(18{x}^{2}\left(9{x}^{2}+5\right)\)
- \(2\left(3{x}^{3}+5\right)\)
- \(2\left(9{x}^{2}\right)\)
Correct

Incorrect
Question 17 of 25

17. Question
Differentiate using the chain rule: \({\left(3{x}^{3}+1\right)}^{2}\)
- \(18{x}^{2}\left(3{x}^{3}+1\right)\)
- \(18{x}^{2}\left(9{x}^{2}+1\right)\)
- \(2\left(3{x}^{3}+1\right)\)
- \(2\left(9{x}^{2}\right)\)
Correct

Incorrect
Question 18 of 25

18. Question
Differentiate using the chain rule: \({\left(5x-7\right)}^{2}\)
- \(10\left(5x-7\right)\)
- \(2\left(5\right)\)
- \(10\left(5+7\right)\)
- \(2\left(5x+7\right)\)
Correct

Incorrect
Question 19 of 25

19. Question
Differentiate using the chain rule: \({\left(6{x}^{2}-6\right)}^{2}\)
- \(24x\left(6{x}^{2}-6\right)\)
- \(2\left(12x\right)\)
- \(24x\left(12x+6\right)\)
- \(2\left(6{x}^{2}+6\right)\)
Correct

Incorrect
Question 20 of 25

20. Question
Differentiate using the chain rule: \({\left(5{x}^{2}+2\right)}^{2}\)
- \(20x\left(5{x}^{2}+2\right)\)
- \(2\left(10x\right)\)
- \(20x\left(10x+2\right)\)
- \(2\left(5{x}^{2}+2\right)\)
Correct

Incorrect
Question 21 of 25

21. Question
Differentiate using the chain rule: \({\left(3{x}^{2}+6\right)}^{3}\)
- \(18x{\left(3{x}^{2}+6\right)}^{2}\)
- \(3{\left(6x\right)}^{2}\)
- \(18x{\left(6x+6\right)}^{2}\)
- \(3{\left(3{x}^{2}+6\right)}^{2}\)
Correct

Incorrect
Question 22 of 25

22. Question
Differentiate using the chain rule: \({\left(7{x}^{3}-6\right)}^{3}\)
- \(63{x}^{2}{\left(7{x}^{3}-6\right)}^{2}\)
- \(3{\left(21{x}^{2}\right)}^{2}\)
- \(63{x}^{2}{\left(21{x}^{2}+6\right)}^{2}\)
- \(3{\left(7{x}^{3}+6\right)}^{2}\)
Correct

Incorrect
Question 23 of 25

23. Question
Differentiate using the chain rule: \({\left(7x-2\right)}^{2}\)
- \(14\left(7x-2\right)\)
- \(14\left(7+2\right)\)
- \(2\left(7x+2\right)\)
- \(2\left(7\right)\)
Correct

Incorrect
Question 24 of 25

24. Question
Differentiate using the chain rule: \({\left(6x+9\right)}^{2}\)
- \(12\left(6x+9\right)\)
- \(12\left(6+9\right)\)
- \(2\left(6\right)\)
- \(2\left(6x+9\right)\)
Correct

Incorrect
Question 25 of 25

25. Question
Differentiate using the chain rule: \({\left(8x+1\right)}^{3}\)
- \(24{\left(8x+1\right)}^{2}\)
- \(3{\left(8\right)}^{2}\)
- \(24{\left(8+1\right)}^{2}\)
- \(3{\left(8x+1\right)}^{2}\)
Correct

Incorrect

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