1. Fall Break Chain Rule Review
AP Calculus
Fall Break Chain Rule Review

2. Calculate the derivative
𝑦= (4 𝑥 2 −5) 4
Calculate the derivative

3. 𝑦 ′ = 32𝑥(4 𝑥 2 −5) 3
Answer

4. Calculate the derivative
f(x)=𝑐𝑜𝑠 (3𝑥+5)
Calculate the derivative

5. f'(x)=−3𝑠𝑖𝑛 (3𝑥+5)
Answer

6. Calculate the derivative
𝑦= 7𝑥 2 −9𝑥+5 𝑥
Calculate the derivative

7. 𝑦′=7−5 𝑥 −2
Answer

8. Calculate the derivative
y= 𝑠𝑖𝑛 3 (5𝑥 −9)
Calculate the derivative

9. 𝑑𝑦 𝑑𝑥 = 15𝑠𝑖𝑛 2 (5𝑥 −9)∙cos⁡(5𝑥−9)
Answer

10. Calculate the derivative
y= 1 𝑠𝑖𝑛3𝑥
Calculate the derivative

11. 𝑦 ′ =−3 (𝑠𝑖𝑛3𝑥) −2 ∙𝑐𝑜𝑠3𝑥
Answer

12. Logs Practice

13. ln 𝑒 6
Evaluate

14. 6 (ln x and e^x are inverses!!)
Answer

15. 𝑒 𝑙𝑛4
Evaluate

16. 3ln2 + 2ln 2 – ln 16
Write as a single log

17. ln 2
Answer

18. Calculate the derivative
f(𝑥)= 4𝑒 𝑥 3
Calculate the derivative

19. f’(𝑥)= 12𝑥 2 𝑒 𝑥 3
Answer

20. Calculate the derivative
y=𝑙𝑛 4𝑥 2
Calculate the derivative

21. y'= 2 𝑥
Answer

22. Calculate the derivative:
1.) y=sin⁡(5𝑥+2) 4
2.) f(x)=4𝑒 𝑠𝑖𝑛5𝑥
3.) g(x)=(𝑙𝑛𝑥)(6𝑥−8) 3
4.) y = 𝑠𝑖𝑛7𝑥 𝑒 𝑥

23. Calculate the derivative:
1.) y=sin⁡(5𝑥+2) 4
y′=20 (5𝑥+2) 3 𝑐𝑜𝑠 (5𝑥+2) 4

24. Calculate the derivative:
2.) f(x)=4𝑒 𝑠𝑖𝑛5𝑥
f′(x)=20𝑐𝑜𝑠5𝑥∙𝑒 𝑠𝑖𝑛5𝑥

25. Calculate the derivative:
3.) y=2 𝑒 𝑥
y′= 𝑙𝑛2∙𝑒 𝑥 2 𝑒 𝑥

26. Calculate the derivative:
4.) g(x)=(𝑙𝑛𝑥)(6𝑥−8) 3
g′(x)= 1 𝑥 (6𝑥−8) (6𝑥−8) 2 (ln⁡𝑥)