1
The Product and Quotient Rules- HW Problems
Find the derivative of the following functions.
1. 𝑓(𝑥 ) = (3𝑥 3 − 4𝑥 + 3)(2𝑥 2 − 4)
2. 𝑔(𝑥 ) = (𝑥 − 3𝑥 2 )(4𝑥 2 + 1)
𝑡4
3. 𝑓(𝑡) =
1−𝑡2
𝑥2 +3𝑥−2
4. 𝑔(𝑥 ) =
𝑥2 −1
3
5. ℎ(𝑡) =
𝑡2
10𝑥7 −2𝑥2
6. 𝑓(𝑥 ) =
2𝑥4
2𝑥4 +5𝑥2 4
7. 𝑔(𝑥 ) =
𝑥3
− 𝑥2
(𝑥2 +1)(𝑥3 −𝑥)
8. ℎ(𝑥 ) =
𝑥2 +2
9. Find an equation of the tangent line to each function at the given
point.
1 1
𝑎. 𝑦= 𝑎𝑡 (−1, )
1+𝑥2 2
𝑥 2
𝑏. 𝑦= 𝑎𝑡 (2, )
1+𝑥2 5
𝑥 1
𝑐. 𝑦= 1 𝑎𝑡 (1, )
𝑥+𝑥 2
The Product and Quotient Rules- HW Problems
Find the derivative of the following functions.
1. 𝑓(𝑥 ) = (3𝑥 3 − 4𝑥 + 3)(2𝑥 2 − 4)
2. 𝑔(𝑥 ) = (𝑥 − 3𝑥 2 )(4𝑥 2 + 1)
𝑡4
3. 𝑓(𝑡) =
1−𝑡2
𝑥2 +3𝑥−2
4. 𝑔(𝑥 ) =
𝑥2 −1
3
5. ℎ(𝑡) =
𝑡2
10𝑥7 −2𝑥2
6. 𝑓(𝑥 ) =
2𝑥4
2𝑥4 +5𝑥2 4
7. 𝑔(𝑥 ) =
𝑥3
− 𝑥2
(𝑥2 +1)(𝑥3 −𝑥)
8. ℎ(𝑥 ) =
𝑥2 +2
9. Find an equation of the tangent line to each function at the given
point.
1 1
𝑎. 𝑦= 𝑎𝑡 (−1, )
1+𝑥2 2
𝑥 2
𝑏. 𝑦= 𝑎𝑡 (2, )
1+𝑥2 5
𝑥 1
𝑐. 𝑦= 1 𝑎𝑡 (1, )
𝑥+𝑥 2
