1. Chain Rule
AP Calculus

2. 𝑦= ( 2𝑥 2 +3𝑥−1) 8
Differentiate

3. 𝑦= ( 2𝑥 2 +3𝑥−1) 8 𝑦 ′ =8 ( 2𝑥 2 +3𝑥−1) 7 (4x+3)
Differentiate

4. 𝑦= cos 3𝑥
Find the derivative

5. 𝑦= cos 3𝑥 y’ = -sin 3x ∙3 y’ = -3 sin 3x
Find the derivative

6. 𝑦= 1 ( 2𝑥 5 −7) 3 y = ( 2𝑥 5 −7) −3 dy/dx = −3 ( 2𝑥 5 −7) −4 ∙ 10𝑥 4 = −30 𝑥 4 ( 2𝑥 5 −7) −4
Find dy/dx

7. 𝑓 𝑥 = 2𝑥+1 𝑥
Find the derivative

8. 𝑓 𝑥 = 2𝑥+1 𝑥 = 2 + 1 𝑥 = 2 + 𝑥 −1 f’(x) = − 𝑥 −2
Find the derivative

9. 𝑔 𝑥 =sin⁡( 𝑥 2 +1)
Differentiate

10. 𝑔 𝑥 =sin⁡( 𝑥 2 +1) g‘(x) = cos( 𝑥 2 +1)∙2𝑥 = 2x cos( 𝑥 2 +1)
Differentiate

11. 𝑦= 𝑠𝑖𝑛 4 𝑥
Find y’

12. 𝑦= 𝑠𝑖𝑛 4 𝑥 y = ( sin 𝑥) 4 y‘ = 4 ( sin 𝑥) 3 ∙ cos 𝑥
Find y’

13. 𝑓 𝑥 = 𝑐𝑜𝑠 2 3𝑥
Find the derivative

14. 𝑓 𝑥 = 𝑐𝑜𝑠 2 3𝑥 f’(x) = 2(cos 3x) ∙(− sin 3𝑥)∙3 f’(x) = -6sin 3x cos 3x
Find the derivative