PRODUCT AND QUOTIENT RULES AND HIGHERORDER DERIVATIVES

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PRODUCT AND QUOTIENT RULES AND HIGHER-ORDER
DERIVATIVES

• Section 2.3

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When you are done with your homework, you should
be able to

• Find the derivative of a function using the
  Product Rule
• Find the derivative of a function using the
  Quotient Rule
• Find the derivative of a trigonometric function
• Find a higher order derivative of a function

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THE PRODUCT RULE

• The product of two differentiable functions f and
  g is itself differentiable.
• The derivative of fg is the first function times
  the derivative of the second, plus the second
  function times the derivative of the first.

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Find the derivative of

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Extension of the Product Rule
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Find the derivative of

• All of the above

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THE QUOTIENT RULE

• The quotient of two differentiable
  functions f and g is itself differentiable at all
  values of x for which .
• The derivative of is the denominator times
  the derivative of the numerator minus the
  numerator times the derivative of the
  denominator, all divided by the denominator
  squared.

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Evaluate and simplify

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Evaluate and simplify

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Evaluate and simplify

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Derivatives of the Remaining Trigonometric
Functions
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Higher Order Derivatives
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Evaluate the third derivative of the function