1. Quotient Rule Polynomials
Silent
Teacher
Intelligent Practice
Narration
Your Turn
𝑑 𝑑𝑥 2𝑥 𝑥−1
𝑑 𝑑𝑥 𝑥 2 −𝑥+5 𝑥 3 −2𝑥−1
Practice

2. Find 𝑑𝑦 𝑑𝑥 of 9 𝑥 2 −1 3𝑥 Find 𝑑𝑦 𝑑𝑥 of 2 𝑥 2 −𝑥 2𝑥
Worked Example
Your Turn
Find 𝑑𝑦 𝑑𝑥 of 9 𝑥 2 −1 3𝑥
Find 𝑑𝑦 𝑑𝑥 of 2 𝑥 2 −𝑥 2𝑥
Differentiate 2 𝑥 2 −2𝑥+1 3𝑥−1
Differentiate 3 𝑥 2 +5𝑥−1 4𝑥+1
The teacher can show both ways of doing these too, via simplifying or via the quotient rule and then simplifying.
@DrChris_Baker

3. 1. 𝑑 𝑑𝑥 4𝑥−1 𝑥 8. 𝑑 𝑑𝑥 4𝑥 𝑥−1 2 2. 𝑑 𝑑𝑥 𝑥 4𝑥−1 9. 𝑑 𝑑𝑥 4𝑥−1 𝑥−1 2
1. 𝑑 𝑑𝑥 4𝑥−1 𝑥
2. 𝑑 𝑑𝑥 𝑥 4𝑥−1
3. 𝑑 𝑑𝑥 𝑥 2 −4𝑥−1 𝑥 2
4. 𝑑 𝑑𝑥 𝑥 2 𝑥 2 −4𝑥−1
5. 𝑑 𝑑𝑥 2𝑥+1 4𝑥−1
6. 𝑑 𝑑𝑥 2𝑥+2 4𝑥−1
7. 𝑑 𝑑𝑥 2𝑥+1 4𝑥+1
8. 𝑑 𝑑𝑥 4𝑥 𝑥−1 2
9. 𝑑 𝑑𝑥 4𝑥−1 𝑥−1 2
10. 𝑑 𝑑𝑥 4𝑥−1 𝑥−1 3
11. 𝑑 𝑑𝑥 −2 𝑥 2 +4𝑥−1 𝑥−1 2
12. 𝑑 𝑑𝑥 5 𝑥 3 −2 𝑥 2 +4𝑥−1 𝑥−1 2
𝑑 𝑑𝑥 4𝑥−1 𝑓(𝑥)
14. 𝑑 𝑑𝑥 𝑓 𝑥 4𝑥−1
@DrChris_Baker

4. 13. 𝑑 𝑑𝑥 4𝑥−1 𝑓(𝑥) = 1−4𝑥 𝑓 ′ 𝑥 +4𝑓(𝑥) 𝑓 𝑥 2
8. 𝑑 𝑑𝑥 4𝑥 𝑥−1 2 =− 4(𝑥+1) 𝑥−1 3
9. 𝑑 𝑑𝑥 4𝑥−1 𝑥−1 2 =− 2(2𝑥+1) 𝑥−1 3
10. 𝑑 𝑑𝑥 4𝑥−1 𝑥−1 3 =− 8𝑥+1 𝑥−1 4
11. 𝑑 𝑑𝑥 −2 𝑥 2 +4𝑥−1 𝑥−1 2 =− 2 𝑥−1 3
12. 𝑑 𝑑𝑥 5 𝑥 3 −2 𝑥 2 +4𝑥−1 𝑥−1 2 = 5 𝑥 3 −15 𝑥 2 −2 𝑥−1 3
𝑑 𝑑𝑥 4𝑥−1 𝑓(𝑥) = 1−4𝑥 𝑓 ′ 𝑥 +4𝑓(𝑥) 𝑓 𝑥 2
14. 𝑑 𝑑𝑥 𝑓 𝑥 4𝑥−1 = 4𝑥−1 𝑓 ′ 𝑥 −𝑓(𝑥) 4𝑥−1 2
1. 𝑑 𝑑𝑥 4𝑥−1 𝑥 = 1 𝑥 2
2. 𝑑 𝑑𝑥 𝑥 4𝑥−1 =− 1 4𝑥−1 2
3. 𝑑 𝑑𝑥 𝑥 2 −4𝑥−1 𝑥 2 = 4𝑥+2 𝑥 3
4. 𝑑 𝑑𝑥 𝑥 2 𝑥 2 −4𝑥−1 =− 2𝑥(2𝑥+1) 𝑥 2 −4𝑥−1 2
5. 𝑑 𝑑𝑥 2𝑥+1 4𝑥−1 =− 6 4𝑥−1 2
6. 𝑑 𝑑𝑥 2𝑥+2 4𝑥−1 =− 𝑥−1 2
7. 𝑑 𝑑𝑥 2𝑥+1 4𝑥+1 =− 2 4𝑥+1 2
@DrChris_Baker