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.