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Product and Quotient Rules and Higher Order Derivatives

Learn the Product Rule and Quotient Rule for finding derivatives of differentiable functions, as well as techniques for finding higher order derivatives. Understand how to apply these rules to simplify derivatives and find the second derivative.

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Product and Quotient Rules and Higher Order Derivatives

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  1. Product and Quotient Rules and Higher Order Derivatives Section 2.3 AP Calc

  2. Thm 2.7 The Product Rule The product of two differentiable functions f and g is itself differentiable. Moreover, the derivative of is the first function times the derivative of the second, plus the second function times the derivative of the first.

  3. For products with more than 2 factors:

  4. Thm 2.8 The Quotient Rule The quotient of two differentiable functions f and g is itself differentiable at all values of x for which . Moreover, the derivative of is given by:

  5. Thm 2.9 Derivatives of Trig Functions

  6. Use the Quotient Rule to prove

  7. Find the derivative:

  8. Characteristics of simplified derivatives: -Absence of negative exponents -Combining of like terms

  9. s(t) v(t)=s’(t) a(t)=v’(t)=s’’(t)

  10. Higher Order Derivatives:

  11. Find the Second Derivative of Find : Find the 2nd Derivative:

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