Chain Rule Silver

Chain Rule Silver

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Question 1 of 25

1. Question
Differentiate using the chain rule: \(\mathrm{cos}\left(5{x}^{2}+3x\right)\)
- -\(\left(10x+3\right)\mathrm{sin}\left(5{x}^{2}+3x\right)\)
- \(\mathrm{sin}\left(50{x}^{3}+30{x}^{2}\right)\)
- \(\left(5{x}^{2}+3x\right)\mathrm{sin}\left(10x+3\right)\)
- \(\mathrm{sin}\left(10x+3\right)\)
Correct

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Question 2 of 25

2. Question
Differentiate using the chain rule: \(\mathrm{cos}\left(5x+5\right)\)
- \(5\mathrm{cos}\left(5x+5\right)\)
- \(\mathrm{cos}\left(-25x-25\right)\)
- \(-\left(5x+5\right)\mathrm{cos}\left(5\right)\)
- \(-\mathrm{cos}\left(5\right)\)
Correct

Incorrect
Question 3 of 25

3. Question
Differentiate using the chain rule: \(\mathrm{sin}\left({x}^{3}+8x\right)\)
- \(\left(3{x}^{2}+8\right)\mathrm{cos}\left({x}^{3}+8x\right)\)
- \(\left({x}^{3}+8x\right)\mathrm{cos}\left(3{x}^{2}+8\right)\)
- \(\mathrm{cos}\left(3{x}^{2}+8\right)\)
- \(\mathrm{cos}\left(-3{x}^{5}-24{x}^{3}\right)\)
Correct

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Question 4 of 25

4. Question
Differentiate using the chain rule: \(\mathrm{cos}\left(x+6\right)\)
- \(1\mathrm{cos}\left(x+6\right)\)
- \(\mathrm{cos}\left(-x-6\right)\)
- \(\left(x+6\right)\mathrm{cos}\left(1\right)\)
- \(-\mathrm{cos}\left(1\right)\)
Correct

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Question 5 of 25

5. Question
Differentiate using the chain rule: \(\mathrm{sin}\left(7{x}^{3}+3{x}^{2}\right)\)
- -\(\left(21{x}^{2}+6x\right)\mathrm{sin}\left(7{x}^{3}+3{x}^{2}\right)\)
- -\(\mathrm{sin}\left(21{x}^{2}+6x\right)\)
- \(\mathrm{sin}\left(147{x}^{5}+63{x}^{4}\right)\)
- \(\left(-7{x}^{3}+3{x}^{2}\right)\mathrm{sin}\left(21{x}^{2}+6x\right)\)
Correct

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Question 6 of 25

6. Question
Differentiate using the chain rule: \(\mathrm{sin}\left(4{x}^{2}+6x\right)\)
- \(\left(8x+6\right)\mathrm{cos}\left(4{x}^{2}+6x\right)\)
- \(\mathrm{cos}\left(32{x}^{3}+48{x}^{2}\right)\)
- \(\left(4{x}^{2}+6x\right)\mathrm{cos}\left(8x+6\right)\)
- \(\mathrm{cos}\left(8x+6\right)\)
Correct

Incorrect
Question 7 of 25

7. Question
Differentiate using the chain rule: \(\mathrm{cos}\left(8x+5\right)\)
- \(-8\mathrm{sin}\left(8x+5\right)\)
- \(\mathrm{sin}\left(-64x-40\right)\)
- \(-\mathrm{sin}\left(8\right)\)
- \(-\left(8x+5\right)\mathrm{sin}\left(8\right)\)
Correct

Incorrect
Question 8 of 25

8. Question
Differentiate using the chain rule: \(\mathrm{cos}\left(3{x}^{2}+6\right)\)
- \(-6x\mathrm{sin}\left(3{x}^{2}+6\right)\)
- \(\mathrm{sin}\left(-18{x}^{3}-36x\right)\)
- \(-\left(3{x}^{2}+6\right)\mathrm{sin}\left(6x\right)\)
- \(-\mathrm{sin}\left(6x\right)\)
Correct

Incorrect
Question 9 of 25

9. Question
Differentiate using the chain rule: \(\mathrm{sin}\left(6{x}^{2}+1\right)\)
- \(12x\mathrm{cos}\left(6{x}^{2}+1\right)\)
- \(\mathrm{cos}\left(12x\right)\)
- \(\mathrm{cos}\left(72{x}^{3}+12x\right)\)
- \(\left(6{x}^{2}+1\right)\mathrm{cos}\left(12x\right)\)
Correct

Incorrect
Question 10 of 25

10. Question
Differentiate using the chain rule: \(\mathrm{sin}\left(9{x}^{2}+2x\right)\)
- \(\left(18x+2\right)\mathrm{cos}\left(9{x}^{2}+2x\right)\)
- \(\mathrm{cos}\left(162{x}^{3}+36{x}^{2}\right)\)
- \(\left(9{x}^{2}+2x\right)\mathrm{cos}\left(18x+2\right)\)
- \(\mathrm{cos}\left(18x+2\right)\)
Correct

Incorrect
Question 11 of 25

11. Question
Differentiate using the chain rule: \(\mathrm{cos}\left(2{x}^{2}+8x\right)\)
- \(-\left(4x+8\right)\mathrm{sin}\left(2{x}^{2}+8x\right)\)
- \(\mathrm{sin}\left(-8{x}^{3}-32{x}^{2}\right)\)
- \(-\mathrm{sin}\left(4x+8\right)\)
- \(-\left(2{x}^{2}+8x\right)\mathrm{sin}\left(4x+8\right)\)
Correct

Incorrect
Question 12 of 25

12. Question
Differentiate using the chain rule: \(\mathrm{sin}\left(2{x}^{2}+6x\right)\)
- \(\left(4x+6\right)\mathrm{cos}\left(2{x}^{2}+6x\right)\)
- \(\left(2{x}^{2}+6x\right)\mathrm{cos}\left(4x+6\right)\)
- \(\mathrm{cos}\left(8{x}^{3}+24{x}^{2}\right)\)
- \(\mathrm{cos}\left(4x+6\right)\)
Correct

Incorrect
Question 13 of 25

13. Question
Differentiate using the chain rule: \(7\mathrm{cos}\left(ln\left({x}^{8}\right)\right)\)
- \(-\frac{56\mathrm{sin}\left(ln\left({x}^{8}\right)\right)}{x}\)
- \(-\mathrm{cos}\left(\frac{8}{x}\right)\)
- \(\frac{56\mathrm{sin}\left(ln\left({x}^{8}\right)\right)}{x}\)
- \(-\frac{56\mathrm{sin}\left(ln\left({x}^{7}\right)\right)}{x}\)
Correct

Incorrect
Question 14 of 25

14. Question
Differentiate using the chain rule: \(7\mathrm{sin}\left(ln\left(x\right)\right)\)
- \(\frac{7\mathrm{cos}\left(ln\left(x\right)\right)}{x}\)
- \(-\frac{7\mathrm{cos}\left(ln\left(x\right)\right)}{x}\)
- \(\mathrm{sin}\left(\frac{1}{x}\right)\)
- \(\frac{7\mathrm{cos}\left(ln\left({x}^{0}\right)\right)}{x}\)
Correct

Incorrect
Question 15 of 25

15. Question
Differentiate using the chain rule: \(4\mathrm{sin}\left(ln\left({x}^{6}\right)\right)\)
- \(\frac{24\mathrm{cos}\left(ln\left({x}^{6}\right)\right)}{x}\)
- \(\frac{24\mathrm{cos}\left(ln\left({x}^{5}\right)\right)}{x}\)
- \(\mathrm{sin}\left(\frac{6}{x}\right)\)
- \(-\frac{24\mathrm{cos}\left(ln\left({x}^{6}\right)\right)}{x}\)
Correct

Incorrect
Question 16 of 25

16. Question
Differentiate using the chain rule: \(5\mathrm{sin}\left(ln\left({x}^{4}\right)\right)\)
- \(\frac{20\mathrm{cos}\left(ln\left({x}^{4}\right)\right)}{x}\)
- \(\frac{20\mathrm{cos}\left(ln\left({x}^{3}\right)\right)}{x}\)
- \(-\frac{20\mathrm{cos}\left(ln\left({x}^{4}\right)\right)}{x}\)
- \(\mathrm{sin}\left(\frac{4}{x}\right)\)
Correct

Incorrect
Question 17 of 25

17. Question
Differentiate using the chain rule: \(6\mathrm{cos}\left(ln\left({x}^{4}\right)\right)\)
- \(-\frac{24\mathrm{sin}\left(ln\left({x}^{4}\right)\right)}{x}\)
- \(\frac{24\mathrm{sin}\left(ln\left({x}^{4}\right)\right)}{x}\)
- \(-\frac{24\mathrm{sin}\left(ln\left({x}^{3}\right)\right)}{x}\)
- \(-\mathrm{cos}\left(\frac{4}{x}\right)\)
Correct

Incorrect
Question 18 of 25

18. Question
Differentiate using the chain rule: \(2\mathrm{cos}\left(ln\left({x}^{7}\right)\right)\)
- \(-\frac{14\mathrm{sin}\left(ln\left({x}^{7}\right)\right)}{x}\)
- \(-\frac{14\mathrm{sin}\left(ln\left({x}^{6}\right)\right)}{x}\)
- \(\frac{14\mathrm{sin}\left(ln\left({x}^{7}\right)\right)}{x}\)
- \(-\mathrm{cos}\left(\frac{7}{x}\right)\)
Correct

Incorrect
Question 19 of 25

19. Question
Differentiate using the chain rule: \(6\mathrm{sin}\left(ln\left({x}^{5}\right)\right)\)
- \(\frac{30\mathrm{cos}\left(ln\left({x}^{5}\right)\right)}{x}\)
- \(\mathrm{sin}\left(\frac{5}{x}\right)\)
- \(\frac{30\mathrm{cos}\left(ln\left({x}^{4}\right)\right)}{x}\)
- \(-\frac{30\mathrm{cos}\left(ln\left({x}^{5}\right)\right)}{x}\)
Correct

Incorrect
Question 20 of 25

20. Question
Differentiate using the chain rule: \(7ln\left(sin\left(2x\right)\right)\)
- \(\frac{14cos\left(2x\right)}{sin\left(2x\right)}\)
- \(\frac{-14cos\left(2x\right)}{sin\left(2x\right)}\)
- \(\frac{7}{2cos\left(2x\right)}\)
- \(\frac{sin\left(2x\right)}{14cos\left(2x\right)}\)
Correct

Incorrect
Question 21 of 25

21. Question
Differentiate using the chain rule: \(9\mathrm{cos}\left(ln\left({x}^{2}\right)\right)\)
- \(-\frac{18\mathrm{sin}\left(ln\left({x}^{2}\right)\right)}{x}\)
- \(\frac{18\mathrm{sin}\left(ln\left({x}^{2}\right)\right)}{x}\)
- \(-\frac{18\mathrm{sin}\left(ln\left(x\right)\right)}{x}\)
- \(-\mathrm{cos}\left(\frac{2}{x}\right)\)
Correct

Incorrect
Question 22 of 25

22. Question
Differentiate using the chain rule: \(4ln\left(sin\left(6x\right)\right)\)
- \(\frac{24cos\left(6x\right)}{sin\left(6x\right)}\)
- \(\frac{sin\left(6x\right)}{24cos\left(6x\right)}\)
- \(\frac{4}{6cos\left(6x\right)}\)
- \(\frac{-24cos\left(6x\right)}{sin\left(6x\right)}\)
Correct

Incorrect
Question 23 of 25

23. Question
Differentiate using the chain rule: \(2ln\left(sin\left(7x\right)\right)\)
- \(\frac{14cos\left(7x\right)}{sin\left(7x\right)}\)
- \(\frac{2}{7cos\left(7x\right)}\)
- \(\frac{-14cos\left(7x\right)}{sin\left(7x\right)}\)
- \(\frac{sin\left(7x\right)}{14cos\left(7x\right)}\)
Correct

Incorrect
Question 24 of 25

24. Question
Differentiate using the chain rule: \(6\mathrm{cos}\left(ln\left({x}^{2}\right)\right)\)
- \(-\frac{12\mathrm{sin}\left(ln\left({x}^{2}\right)\right)}{x}\)
- \(-\mathrm{cos}\left(\frac{2}{x}\right)\)
- \(\frac{12\mathrm{sin}\left(ln\left({x}^{2}\right)\right)}{x}\)
- \(-\frac{12\mathrm{sin}\left(ln\left(x\right)\right)}{x}\)
Correct

Incorrect
Question 25 of 25

25. Question
Differentiate using the chain rule: \(6\mathrm{cos}\left(ln\left({x}^{6}\right)\right)\)
- \(-\frac{36\mathrm{sin}\left(ln\left({x}^{6}\right)\right)}{x}\)
- \(\frac{36\mathrm{sin}\left(ln\left({x}^{6}\right)\right)}{x}\)
- \(-\mathrm{cos}\left(\frac{6}{x}\right)\)
- \(-\frac{36\mathrm{sin}\left(ln\left({x}^{5}\right)\right)}{x}\)
Correct

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