ACTIVITY 1
Objectives:


To help the students understand the basic concept of derivatives.
To help students recall the fundamentals of algebra and trigonometry.
Differentiate the following functions. Use only the definition of derivatives.
1. 𝑦 = 𝑥 3 − 2𝑥 2 + 6
2. 𝑦 = 𝑥 4 − 2𝑥 3
1
3. 𝑥 = 2 𝑡 4 − 5𝑡 − 3
1
2
4. 𝑦 = (3𝑥 2 + 1)2
5. 𝑦 = (𝑥 2 − 2)2
6. 𝑦 =
7. 𝑦 =
8. 𝑥 =
1
𝑥+7
1
4−𝑥
2𝑦
𝑦−1
9. 𝑦 = 2 − 3𝑥 −
3𝑥−1
10. 𝑦 = 2𝑥+5
1
11. 𝑥 = 𝑡 2
12.
13.
14.
15.
𝑦 = √𝑥 + 2
𝑦 = 𝑥√𝑥 − 1
𝑦 = 𝑐𝑜𝑠 2 3𝑡
1−cos 4𝑥
𝑦=
1+cos 4𝑥
1
𝑥