1. 2.4 Product and Quotient Rules
Calc 10/3/14

2. Warm-up 2.4 Product and Quotient Rules
Welcome future entrepreneurs and economists!
What price should we sell this product for?
(The demand function comes from our extensive research of past sales and consumer surveys)

3. 2.4 The Product and Quotient Rules
𝑓(𝑥)= 3 𝑥 𝑥 −5
𝑓 𝑥 = 4 𝑥 2 −7𝑥+18 𝑥 2

4. The Product Rule
The derivative of the product of two differentiable functions is equal to the first function times the derivative of the second function plus the second function times the derivative of the first.
𝑑 𝑑𝑥 𝑓 𝑥 𝑔 𝑥 =𝑓 𝑥 𝑔 ′ 𝑥 +𝑔 𝑥 𝑓′(𝑥)

5. Ex 𝑦= 3 𝑥 𝑥 −5
Find the value of the derivative at (1, -28)

6. Ex 2. 𝑦=(6−3𝑥)(4𝑥+3 𝑥 2 )
Find the value of the derivative when x=2

7. Ex 3. y=( 2 𝑥 +1)(3𝑥 −1)
Find the value at (4, 16.5)

8. Ex 4. 𝑦=3𝑥(2 𝑥 2 +5𝑥)

9. 𝑑 𝑑𝑥 𝑓 𝑥 𝑔 𝑥 = 𝑔 𝑥 𝑓 ′ 𝑥 −𝑓 𝑥 𝑔 ′ 𝑥 𝑔 𝑥 2
The Quotient Rule
The derivative of the quotient of two differentiable functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
𝑑 𝑑𝑥 𝑓 𝑥 𝑔 𝑥 = 𝑔 𝑥 𝑓 ′ 𝑥 −𝑓 𝑥 𝑔 ′ 𝑥 𝑔 𝑥 2

10. Ex 5. 𝑦= 𝑥+4 5𝑥−2

11. 𝐸𝑥 𝑦= 3− 2 𝑥 𝑥+4

12. Ex 7 a) 𝑦= 5 𝑥 b) 𝑦=− 3 3𝑥−2 𝑥 2 7𝑥

13. BE CAREFUL
Product Rule does NOT mean to multiply the derivatives of each
Quotient Rule does NOT mean to divide the derivatives of the numerator and denominator
If you can use the constant multiple rule….
Use it! Saves you a lot of time and effort