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Some Differentiation Rules- HW Problems
Find the derivative of the following functions (where they are defined).
1. 𝑓(𝑥 ) = 𝑥 10
2. 𝑔(𝑥 ) = 𝑥 3 − 3𝑥 + 10
3. 𝑓(𝑡) = 𝑡11 + 2𝑡 9 − 6𝑡 3 + 3
4. 𝑔(𝑥 ) = 320
4𝑡5
5. 𝑓(𝑡) = −
5
6. 𝑔(𝑥 ) = (2𝑥 2 + 1)(3𝑥 3 + 𝑥)
7. 𝑓(𝑥 ) = 𝑥 (𝑥 2 + 3) + (𝑥 2 + 2)(𝑥 − 2)
3𝑡6 −4𝑡8
8. 𝑓(𝑡) =
2𝑡3
(𝑥 2 −1)(𝑥 3 +3𝑥)
9. 𝑔(𝑥 ) =
𝑥 2 −𝑥
10. Let 𝑓(𝑥 ) = 𝑥 3 + 3𝑥 2 − 9𝑥 + 2. At what value of 𝑥 does the slope
of the tangent line to the graph of 𝑦 = 𝑓(𝑥) equal 0?
11. Find the second derivative of the following functions.
5𝑥2
𝑎. 𝑓 (𝑥 ) = 𝑥 8 − 2𝑥 5 + − 2𝑥 + 1
2
𝑏. 𝑦 = 2𝑡 4 − 3𝑡 2 − 𝑡 + 6
12. Let 𝑓(𝑥 ) = 𝑥 4 − 6𝑥 2 . For what values of 𝑥 is 𝑓 ′′ (𝑥 ) = 0?
Some Differentiation Rules- HW Problems
Find the derivative of the following functions (where they are defined).
1. 𝑓(𝑥 ) = 𝑥 10
2. 𝑔(𝑥 ) = 𝑥 3 − 3𝑥 + 10
3. 𝑓(𝑡) = 𝑡11 + 2𝑡 9 − 6𝑡 3 + 3
4. 𝑔(𝑥 ) = 320
4𝑡5
5. 𝑓(𝑡) = −
5
6. 𝑔(𝑥 ) = (2𝑥 2 + 1)(3𝑥 3 + 𝑥)
7. 𝑓(𝑥 ) = 𝑥 (𝑥 2 + 3) + (𝑥 2 + 2)(𝑥 − 2)
3𝑡6 −4𝑡8
8. 𝑓(𝑡) =
2𝑡3
(𝑥 2 −1)(𝑥 3 +3𝑥)
9. 𝑔(𝑥 ) =
𝑥 2 −𝑥
10. Let 𝑓(𝑥 ) = 𝑥 3 + 3𝑥 2 − 9𝑥 + 2. At what value of 𝑥 does the slope
of the tangent line to the graph of 𝑦 = 𝑓(𝑥) equal 0?
11. Find the second derivative of the following functions.
5𝑥2
𝑎. 𝑓 (𝑥 ) = 𝑥 8 − 2𝑥 5 + − 2𝑥 + 1
2
𝑏. 𝑦 = 2𝑡 4 − 3𝑡 2 − 𝑡 + 6
12. Let 𝑓(𝑥 ) = 𝑥 4 − 6𝑥 2 . For what values of 𝑥 is 𝑓 ′′ (𝑥 ) = 0?
