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Derivatives and Functions Flashcards | StudBud

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Derivatives and Functions

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Explore questions about finding derivatives and evaluating functions in calculus

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Questions 10

Answers

1
Find 𝑘′(𝑥) for 𝑘(𝑥) = (3𝑥² + 5𝑥)(4𝑥² + 3𝑥)
24𝑥³ + 39𝑥² + 15𝑥
12𝑥³ + 39𝑥² + 15𝑥
12𝑥³ + 39𝑥² + 30𝑥
24𝑥³ + 39𝑥² + 30𝑥
2
Find 𝑦′ for 𝑦 = tan(5𝑥³)
15𝑥sec²(5𝑥³)
5𝑥sec²(5𝑥³)
5𝑥²sec²(5𝑥³)
15𝑥²sec²(5𝑥³)
3
Find 𝑦′ for 𝑦 = (5𝑥² + 3𝑥)⁴ / (𝑥² + 4)
10𝑥(5𝑥² + 3𝑥)² / (𝑥² + 4)
20𝑥(5𝑥² + 3𝑥)² / (𝑥² + 4)
20𝑥(5𝑥² + 3𝑥)³ / (𝑥² + 4)2
2x3(5x+3)3(15x3+3x2+80x+24)/(x2+4)2
4
Find 𝑓′(𝑥) for 𝑓(𝑥) = sin(2𝑥³)
6𝑥²cos(2𝑥³)
6𝑥cos(2𝑥³)
2𝑥²cos(2𝑥³)
2𝑥cos(2𝑥³)
5
Find [𝑓(𝑥) − 𝑔(𝑥)]′ for 𝑓(𝑥) = 7𝑥³ − 6𝑥² and 𝑔(𝑥) = 6𝑥² + 8𝑥
21𝑥² − 20𝑥
7𝑥² + 20𝑥
21𝑥² + 20𝑥
7𝑥² − 20𝑥
6
Find 𝑓′(𝑥) for 𝑓(𝑥) = 2𝑥⁻³ / (5𝑥² − 3𝑥 + 2)
25x2-24x+12/ (5𝑥² − 3𝑥 + 2)2
6𝑥⁻³ / (5𝑥² − 3𝑥 + 2)
50x2-24x+12/x4(5x2-3x+2)2
-6𝑥⁻³ / (5𝑥² − 3𝑥 + 2)
7
Find 𝑓′(𝑥) for 𝑓(𝑥) = 6𝑥² − 5𝑥 + 7
6𝑥 − 5
12𝑥 + 7
6𝑥² − 5
12𝑥 − 5
8
What is 4𝑓′(𝑥) for 𝑓(𝑥) = 2𝑥⁴ − 3𝑥³ + 5𝑥² + 4?
32𝑥³ − 36𝑥² + 40𝑥
8𝑥³ − 9𝑥² + 10𝑥
8𝑥³ − 9𝑥² + 20𝑥
32𝑥³ − 36𝑥² + 20𝑥
9
Find 𝑦′ for 𝑦 = (𝑥³ + 3)⁵
15𝑥(𝑥³ + 3)⁴
5𝑥²(𝑥³ + 3)⁴
5𝑥(𝑥³ + 3)⁴
15𝑥²(𝑥³ + 3)⁴
10
Find (𝑓𝑔)′ for 𝑓(𝑥) = 𝑥 + 3 and 𝑔(𝑥) = 2𝑥 − 5
2𝑥 − 3
2𝑥 − 1
2𝑥 + 3
2𝑥 + 1