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Derivative Warm-ups

This resource offers warm-up exercises focused on derivatives, ideal for AP Calculus students. It covers essential concepts like amplitude, vertical shift, phase shift, and period in trigonometric functions, exemplified by exploring the equation ( y = 3 cos(x) + 2 ). It also includes various derivative rules, such as the product rule and quotient rule, to help students practice finding derivatives of functions. Gain confidence in applying these rules through targeted warm-up problems designed to reinforce understanding of calculus concepts.

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Derivative Warm-ups

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  1. Derivative Warm-ups AP Calculus

  2. Write the equation of the function:

  3. Amplitude: Half of distance of 6 between max/min Vertical shift: Halfway between min (-1) and max (5): Avg is (-1 + 5)/2 = 2 Phase shift: None (left/right) Period: 4. To solve for k: = 4. Solve for k. y = 3 cos( x) + 2

  4. Evaluate: cos

  5. Derivative Warm-ups ln

  6. Derivative Rules Chain Rule: Logs/Exponentials =

  7. Product Rule Practice Find each derivative:

  8. Product Rule Warm-up Find dy/dx:

  9. Product Rule/Exponentials Review

  10. Quotient Rule Alternate def (u and v are functions of x):

  11. Derivative Rules Chain Rule: Logs/Exponentials =

  12. Derivatives Warm-up Find the derivative using the Quotient Rule:

  13. Trig Derivatives Warm-up

  14. Trig function derivatives

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