The Quotient Rule
Objective To use the quotient rule for differentiation. ES: Explicitly assessing information and drawing conclusions
The Product Rule Does ? NO! Take each derivative
The Quotient Rule Does ? NO
The derivative of a quotient is not necessarily equal to the quotient of the derivatives. The Quotient Rule
The derivative of a quotient must by calculated using the quotient rule: Low d High minus High d Low, allover Low (low squared)
The Quotient Rule 1.Imagine that the function is actually broken into 2 pieces, high and low.
The Quotient Rule 2. In the numerator of a fraction, leave low piece alone and derive high piece.
The Quotient Rule 3. Subtract: Leave high piece alone and derive low piece.
The Quotient Rule 4. In the denominator: Square low piece. This is the derivative!
The Quotient Rule Final Answer
The Quotient Rule Low d High minus High d Low, allover Low (low squared)
Final Answer Example A: Find the derivative Low d High minus High d Low, allover Low (low squared)
Final Answer Example B: Find the derivative Low d High minus High d Low, allover Low (low squared)
Example C: Find the derivative Final Answer Low d High minus High d Low, allover Low (low squared)
Example D: Find the derivative Final Answer Low d High minus High d Low, allover Low (low squared)
Example E: Find the derivative Low d High minus High d Low, allover Low (low squared) Product Rule for D’Hi
The Quotient Rule Final Answer
The Quotient Rule Remember: The derivative of a quotient is Remember: The derivative of a quotient is Low, D-High, minus High, D-Low, all over the bottom squared.